If you have an Nvidia card, make sure you're using VDPAU off-loading. In mplayer, this is done with the -vc argument:

mplayer -vc ffh264vdpau -fs /path/to/your/file

Without VDPAU, you'll need a lot more CPU horsepower to play the stream smoothly. For example, a E4500 @ 2.20GHz cannot keep up with heavily encoded x264 1080p streams without VDPAU. An Intel video card on a 2GHz system isn't going to work, I don't think. :(

Maybe your laptop has a weak graphics card or heat problems. What does totem do?

Even when there is no such a "Minimal requirements" for h264 video playback (the audio is not your problem at this time), you should consider using a high performance GPU in order to experience the best results on your playback.

Information provided in the answers to this question may give you an idea of what a hardware I am talking about. Of course, I am for nVidias (1GB or more) but you can choose a different brand name. Anyway, Intel embedded graphic cards won't achieve a smooth playback for high demanding video codecs (like h264).

Your microprocessor is good enough for a smooth playback but you may be experiencing an issue at the moment that your computer needs to "draw" the things on screen. Task that is normally achieved by the GPU, not the CPU itself. When I answered this question I was using a microprocessor similar to yours, with a PhysX SPARKLE GeForce 9500GT 1024MB/DDR2/CRT/DVI-I/HDCṔ/SLI/PCI Express 2.0 and experiencing no problems during the playback.

Smooth fullscreen 1080p playback

Placed here for your convenience:

The minimum? What a question.

I have several nVidia based graphic cards with both 512 MB and 1024 MB in different systems, and both are good for playing high definition video files. The best, of course, is the 1024 MB card, which is not expensive at all.

You may experience a better performance starting at 1024 MB video card. And I am talking to those times when you wish to play a high definition video and do something else. Or when using two monitors to extend the desktop, etc.

There are new video cards with DDR3 memory systems which will absolutely work better than DDR2 memory based systems.

I prefer the nVidia's but I know that ATI's are also good and many people prefer ATI over nVidia and I have seen an ATI RADEON with 3 GB memory system at work, owned by a gamer friend.

Take in consideration that any video card starting at 1024 MB memory system will do the work with ease.

My nVidia models are:

1. ZOGIS GeForce 8500GT 512MB DDR2 PCI Express
2. PALIT 9500GT Super 512MB/128Bit/DDR2 Dual Link DVI/TV-Out PCI Express 2.0
3. PNY VERTO GT220 1024MB DDR2 PCI Express

And my favorite and the one that I am using when writing this is the:

• PhysX SPARKLE GeForce 9500GT 1024MB/DDR2/CRT/DVI-I/HDCṔ/SLI/PCI Express 2.0

This graphic card features no fan and a big aluminum heat sink, which makes absolute silently performance and you won't face the problems when the fan fails because of the dust or typical problems on the fan.

In this link you can find a screen recording of my system when playing a RAW mpeg HD Video file when using dual monitor view. (Take in consideration that I am running in a 2GB RAM system and the screen capture may differ of what I see on this side).

The video is played windowed and full screen in my left side monitor.

For download only, at: http://geppettvs.servehttp.com/resources/desktop.ogv (right click, save target as)

In VLC, Menu "Media" and "Open Network Stream", enter the url and click "Play".

The specs of the video file can be seen in the next screenshots.

My current monitor config in the next screenshot:

Additionally, the comments on the original answer will be very illustrative also.

Good luck!