Intel has a line of integrated graphics controllers, mainly for notebooks and budget desktops; they've had open-source 2D and 3D drivers on X.org/Mesa for quite awhile now.

Thanks for reply,

but I need a card for an existing PC, which graphicadapter let the system crash somehow.

Are the Intel chipsets onboard only? I only see Nvidia/ATI, and if I'm lucky some XGI and Matrox cards. None from Intel.
And have they released the full documentation?

The Radeon 9200 series is about the strongest dedicated card currently which has entirely Free driver support through the Mesa/DRI stack. I've got one in my box and it kicks a lot of butt. It's not exactly powerful in comparison with the current cards on the market, but it gets the jobe done quite well (and plays games like BZFlag, Neverball, Quake 3, etc. at their near-highest settings quite smoothly). :)

Don't get the "SE" or "LE" cards though, as those have half the memory bandwidth and/or lower GPU clock speeds, respectively. You'll need X11R7 and a recent kernel DRM layer if you want to use it in 8x AGP mode, but the performance difference between 8x AGP and 4x AGP is minimal since this card can't push much extra through that bandwidth, anyway. Hope that helps!

Using MergedFB (which it will auto-detect in most cases), it can do hardware-accelerated 2D and 3D up to 2048x1536 at 85Hz, according to ATI's and the DRI project's websites.

There's a serious problem with ATI & xv though, and it hasn't been fixed now for a long time: you can't play video streams wider than 1536 pixels with the overlay. That's pretty bad for movies in 1080i HD. There will just be a pink bar between the 1537th and the 1920th column.
This also means one has no access to the card's built-in scaling, so I'm converting to 1280x720 for my projector with mplayer's software scaler, which nearly maxes out the CPU (P4 3 GHz).