I put an ASUS EN6200TC in my quiet PC about six months ago. It was a generation (now two) behind the bleeding (and screaming) edge but it performs quite satisfactorily for me and has no fan which makes it a winner. Unfortunately it is PCIe.
Don't get a GeForce FX5xxx, they are brutally slow.
Assuming you want at least one DVI output the ASUS N6200 (GF6200 with 128MB for $60) looks like a reasonable (again, two generations behind, but not actually a bad chip, and the card is fanless) solution. If you prefer an ATI chipset, you can get a fanless 9600 from Sapphire for $67 on Newegg.
Note that with a fanless board you do have to worry somewhat about the airflow in the video card area. A severely cramped or poorly designed case might pose problems even though these cards do run relatively cool. But if you think you can pull it off I highly recommend it, as video card fans tend to be by far the loudest component of any otherwise well-made system.
edit: apparently I can't post links
, look for any of the parts i've listed on froogle or newegg.