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Skype: S stands for 'suck'
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Skype's "S" stands for "Suck"

Skype sucks, truly. First its user interface is far from being the best (Windows 8 Metro style), its memory consumption is just too high (more than 128 MB when idling), and the fact that at some point everybody experiences the "I can't hear you"/"Can you hear me?" problem ultimately shows something's wrong.
Despite all the rant people and I('m gonna) make, Skype, until then, had a great success among friends, families, or even whole companies. Even before Microsoft started to replace Windows Live Messenger with Skype. To be honest, Skype, before they got bought, did a fairly good job.
Skype sucks, here's why:

In-application advertising

Whose idea is it, seriously? Back when Skype was independent, using advertising to keep their servers up was one of the few, if not only, options. Now that Microsoft bought the company, keeping servers running is no more a problem, yet they intentionally let the ads. Why is that? Stangely enough, these ads aren't present on the Windows 8/RT version, nor on Linux; probably because they rely on a crappy technology, id est Adobe Flash, to display them, which is just extremely heavy given the *cough* performance of Flash.
Android suffers of another problem: consider the screenshot to the right. "Nouveau message" means "New message" in French. Looks legit, doesn't it? Using the same colors as the app, it easy gets people into touching the ad. Clever technique, touch well earned, but that's called clicktouchjacking, and should be considered illegal as it is nowhere written explicitly that this is an ad. After opening the ad, it generally asks to send a text to a surchared special number (which puts the sender in an expensive, hardly cancellable subscription) or downloads an APK greedy on permissions (i.e. requesting every possible one) which basically is a botnet or something of the same kind.
Clickjacking ads on mobile & Flash-based ads on PC = crap & lag full throttle! See image on right: "Nouveau message" ("New message") seems legit but is not.

Going back and forth

The huge service that is Skype ovbiously need servers to run, either to redistribute updates, store all the accounts, etc... During its infancy, it tried to rely a minimum on a centralized model, to avoid the cost of setting up and maintaining new servers, and to save bandwidth. From a privacy point of view, it was really positive. The only big downside to this approach is that some computers with enough bandwidth and processing power could become a "supernode" on user's behalf:
You hereby acknowledge that the Skype Software may utilize the processor and bandwidth of the computer (or other applicable device) You are utilizing, for the limited purpose of facilitating the communication between Skype Software users.
Old Skype EULA, §4.1
This wasn't an option, so well-served places such as universities began blocking Skype.
Beginning with Microsoft's merger, it began stepping back. They have their reasons (performance mainly), but they definitely include collaboration with intelligence agencies. Supposedly, MS set up thousands of Linux-based boxes to replace the supernode's role... did they admit their blatant server OS defeat? Even if Microsoft appears to be more friendly to Linux, it still and will still have plans for keeping it under the table on the desktop market (e.g. UEFI Secure Boot), and same on the server market, although MS knows they already lost the battle. Don't even mention Linux on Azure, smoke and mirrors, that's all.
Skype had no money, gets clients to be "supernodes" (servers) for them. Then MS happened, and whole centralized model now.

Data leakage, by design

Though we know Skype uses end-to-end encryption such as 256-bit AES, assume it simply does not. When you send a link during a text conversation and the specific URL gets pinged by Microsoft afterwards, you may have some doubts. Actually, the paragraph 8 of Skype's EULA states that our data can be accessed by Microsoft or its affiliates, subsidiaries or service providers, which is of course vague, and used in automated scanning that supposedly prevent spam/phishing but hilarously fails at this (but by itself is a good intention). The most scary sentence is the last:
Skype may, in its sole discretion, block or prevent delivery of suspected Spam, and remove suspicious links or content from messages.
Skype EULA, §8.1
What do we learn? Not only they can entirely block messages, but they can also alter it as they please, given the so-called "suspicious links or content" definition is entirely up to them.
Back in 2012, it was dead easy for anybody to find your IP even if he/she is not in your contact list if you were connected. This *cough* bug was since fixed, hopefully, but it made clear that behind the so-called security of the software was a big hole. Though parts of the hole has been filled since, it makes no doubt Skype is still not secure.
Examples of why Skype can't be trusted:
Skype claims encrypted & secure chat? I call for bullshit:

Poor design

Skype, in its (now roughly) ubiquitous nature, should be as lightweight as possible so it runs well even on old hardware. Think of all the old PCs still running on Windows XP... Yet it easily eats 128MB of RAM, and many people complain about this (1,2,3,4,5,...), but a common and not even barely real response is to say that "it's because you're a supernode", sure, on and old 900MHz Pentium III XP box with 8 Kb/s of upload speed. I call for bullshit.
Hey, can you hear me? I don't hear you either
Every grandma calling her grandson on Skype
Apart from the (quite frequent) bad audio setups & configurations, this happen way too often, and way too often the solution is completely dumb: Skype chose the bad audio input/output device. Sure it doesn't know which device is supposed to be used, but since the incorrect devices always make no sound at all, Skype could check the audio data and warn the user about a possible misconfiguration or muted microphone. And yes, there is a Skype setup guide, but somehow we all have problems later (hey, plug in that new shiny microphone!).
gravgun, robot voice!
Any of my friends after 10 minutes of Skype-ing
The issue I face seems Linux-specific: after roughly 10 minutes of Skype conversation, my audio becomes all garbled, and it doens't come back. Whereas any other applications records sound perfectly even once the garbling starts, and for hours, without any issue except Audacity which has bad PulseAudio support. I suppose it is somehow related to bandwidth-fitting... and it is honestly bad; Skype falls back gracefully to a lesser-quality audio by lowering the bitrate of its SILK codec, but once the network regains its efficiency (e.g. finished downloading a file), it can take forever to get back to a good sound quality.
The General User Interface (GUI) is... good. "Good", not "excellent"; for instance the contact search form is a separate window whereas it should be the UI's right pane. And there are other bits people may complain about, such as the eye-hurting too contrasted and too squared look of Windows 8 design backported to Windows 7 and less.
A major PITA is when you want to interact with someone not in your contact list. Standard chat and voice talk works fine, but any other feature requires you to go through the painful process of asking that person to be your Skype friend. E.g. the other person wants to start a group talk from a simple 2-peer talk, he/she can't.
Last huge bad design is lack of features. Not in a general sense, but in a device-specific sense. The reference Skype implementation is, of course, the Desktop Windows version, and other versions simply lack some features that are not reported as unsupported to any peer. The group call features are told as not being available if any of the call's peers doesn't support it, hopefully, yet some less-known features such as "Send contacts", and mainly recieve them are deliberately missing from Android and iOS versions at least.
If all of this was to be fixed, I would be happy. "would", because I'll actually not give a shit about it, Skype is and will always be proprietary crap.
Skype: RAM and CPU eater, shit support for everything except Windows.

Anti-competitiveness at its best

Skype is closed source, OK, we all know that. Not even the slightest move towards interoperability, you know, that word that MS emphasises on but only apply to their own products. Skype's communication protocol is not innovative at all, as other voice chat application already do the same (e.g. Google Hangouts, SIP, Tox), and no, encryption is not hard to implement on a protocol. And no work is being done to at least provide an API for developers to use and interact with Skype services (not talking about the client COM API here).
Moreover, Skype only works (really) well on Windows, thus Microsoft is silently pushing every Skype user to use it to get good support and features, even if we can't (i.e. money, non-supporting hardware). This is amplified by the network effect: as more and more people use Skype and the fact that is not interoperable, more and more people... uses it because their frends/family/boss uses it.
While it is not widely know, there actually was some effort made to make Skype more open, but ovbiously not by MS. This effort was led by a Russian hacker named Efin Bushmanov. He reverse-engineered and deobfuscated the Skype binaries bits by bits, up to version 5, to finally be able to understand most parts of the protocol. All his work was put on his Blogspot blog and on GitHub.
Then mighty Microsoft came and ruined his work, and our hope for a more open Skype. Here's a link to his blog, come on, look at it. Hopefully, the amazing guys from Web Archive did fetch an old version, which is still available here!
His GitHub repo was also taken down, and until recently GitHub took down whole repositories even when only one (or more) file was affected by the DMCA notice; and MS complained about a zip file redistributing Skype 5.5, that's all; but it was clear their intent was to take down all Efin's work.
<irony> Thanks Microsoft, you saved us all! </irony>
Russian hacker Efin Bushmanov was supposed to be our saviour, but MS guys are fucking bastards.

They're just children, after all

This is more recent. To be short, I lol'd hard when reading this; Skype Chief Executive quits MS. While I understand, on an invidual level, that you may want to go after the recent media coverage of NSA (& friends) global spying, the natural involvement of MS's Skype division, etc, this behavior is just childish; I'm sorry to say that, at least that's how I percieve it.
lol look we're evrywhere in da news, they say bad things about us, i dont want to endure this omg omg omg bye guys xoxoxo
How I imagine previous Skype Chief Executive when he left (yes this is ridiculous)
Have a Windows Phone 7 phone? You ain't getting any Skype, because they're too lazy to keep it up on WP7. C'mon guys, it's your own mobile OS...
Skype Chief Executive quit MS under media pressure about mass spying, being total kid. Also, no Skype on Windows Phone 7, WTF?

What to use then?

Virtually anything you want. Until you begin to rant about it too.
But ideally, choose something that respects your privacy, i.e. really does and therefore is decentralized and open source, such as Tox. Tox also has the (dis?)advantage of requiring no sign-up process; you download a Tox client (Tox by itself is only the core), open it up and bang, you have an identity which looks like ...
CFB5EA4121F9131D340024E84AB739ADDB3293ED0D3D38EA7097C9A218ED254D1E042BA5B8DE, that's 76 mothereffin' characters! Hopefully solutions are being worked on to provide usernames, and will become effective in the future. Fow now, we have toxme.se and utox.org who provides a username feature, but as they are separate (but functionally identical) services, you can have both username@toxme.se and username@utox.org linking to different IDs.
Another "issue" is the current Tox status: it is still in heavy development. At the time of writing, Tox has issues with audio group chats with 20+ participants. Many other little issues and bugs are still to be fixed, the design can change quite rapidly and clients have to follow. Oh darn, clients too: uTox and qTox are the most popular on desktop, but none of them supports the full range of Tox features yet. So choose any of them, as you like. It's still better than Skype on the points I cited up there.
Use Tox.

Some people has already quit Skype

I did and so should you