Problems to play HD and HFR videos.

ATI and AMD cards are all crap with free software. None of them support 3-D acceleration. Assuming you're able to play these kinds of videos on non-free systems, probably your card just doesn't have support for hardware-accelerating video playback without non-free software. It could be solved much like the problem with Nvidia cards if there was a reverse-engineering effort, but as far as I know there is not a major effort to reverse-engineer these GPUs. I guess a lot of people are satisfied with AMD's bullshit half-cooperation.

The best GPUs are Intel integrated graphics (e.g. Intel GMA or Intel HD), which their manufacturer provides free drivers for, and older Nvidia cards, which the Nouveau project have done a good job reverse-engineering.

That's what I was thinking :(
If it was a desktop, I would have no problem. But with a laptop, I can't really replace the graphics card. Which, by the way, is a very powerful one, I admit. I remember when I used to have the proprietary drivers, I could play very graphic intense games, it was able to play HD stuff very well, all of that... the problem is really the lack of a proper free driver. One of these days, I discovered that even using the HDMI to connect to a TV was basically... impossible.

I was thinking that maybe I could get around by using some lighter software (I don't know if SMplayer is heavy on the machine or not) that could play those using only the CPU and not using the graphic card so much... But apparently no :(

Thanks anyway Onpon4.

If the videos being HD isn't needed, you could of course size the videos down. WinFF can do that, and I'm sure there are others.

The best option for video decoding simply is Intel graphical chipsets, which are integrated to their CPUs. If we are talking about a desktop computer with an Intel CPU, just remove the AMD/ATI video card for better performances, 3D acceleration and a lesser energy consumption!

If you stick to the AMD/ATI card, you can easily get a newer kernel and a newer graphical stack with Trisquel 6.0 (those back-ported from Ubuntu 13.10). Try to install the following packages (e.g., with the Synaptic package manager) and reboot:
linux-generic-lts-saucy
libegl1-mesa-lts-saucy
libgles1-mesa-lts-saucy
libgles2-mesa-lts-saucy
xserver-xorg-lts-saucy

For Debian, well, ask on Debian's forum...

To play 1080p videos you'll need the following (tested on Trisquel 6.0 32bits):

* processor: 2.7Ghz (I guess about 2.3Ghz would be OK too).
* Graphics Card: 32MB video RAM (it can be shared memory, I've tested with shared memory, obviously onboard card). Decent CUDA and base clock speed.
* Memory: 512MB DDR2 800Hzs (using 64bits OS will need more RAM | better using 2 x 256MB).
* North and South bridge with sufficient speed.
* Gnome Player/Totem as in Trisquel default. Most of the videos will play good but at some part like a lot of rain plus quick movements it could not run smoothy but after that it can "recover" from that. Unfortunately the best HD video player is non free and for Windows (MPC) because it makes a good use of codecs. Linux best player for this is Gnome Player/Totem. Worst player ever for this is VLC (also in Windows).
* Drivers: You DO need to use the drivers or it won't play smooth at all. I've always played with drivers working on nVIDIA chipsets. I'd say that almost no one ATI will work good to play HD.
* Kernel: I've always used Trisquel default kernels. linux-libre 3.2 is okey. Note that if have the right drivers it doesn't mean you will be able to play HD videos because those drivers also need to be well integrated to the kernel.

BTW, Post more specifications on the hardware you're running.

Above the minimum requeriments I mention before to 1080p everyone should be fine but I can't say on ATI or Intel if that needs are the same for those graphic cards.
Note that 1080p differs from 1080i. And on 60fps you'll need a lot more of the minimum requierements I wrote to play them.

Playing HD and HRF videos it's not about capacity, it's about speed.

I would try to set up a minimal desktop environment and kill all unneccesary processes; perhaps with a very fast video player it will work.

I recommend using xmonad together with mplayer.
So do a
apt-get install xmonad mplayer
then logout and choose "xmonad" as a desktop session.
You'll see nothing but a blank screen or maybe a wallpaper.
Hit "alt+shift+return" to open a terminal.
Then type "mplayer /path/to/your/file.webm".

You can first try to checkout which processes are running with "top" and kill everything redundant.

Thanks everyone who tried to give some help.
I have decided against making any major changes in my system for the purpose of playing these videos. I don't have a lot of them, and I really want to keep my system clean and stable as it is right now. Totem video player has shown to be a better option for playing HD videos than SMPlayer, so I will use it instead (even if not a perfect playback, but it's tolerable). HFR is a different story, I will see into those later (maybe convert them as someone suggest, making them SD HFR instead of HD).
Thanks everyone for the comments :)