There seem to be some bugs with AMD/ATI card, their support still needs improvement.
Having maxed out all visual options (expect FSAA that is deactivated by the game...), i get crashes in heavy ground combats (AMD 4870 1GB, game freezes, returning to desktop, everytime sending a 850MiB memory dumb ^^).
Turning of bloom and dyn lightning helps out. Furthermore there are some shadow map flicker bugs if you turn the camera to have the PoV like being the primary light source and zoom in to the max on the ship (only the faces of the ship that have a angle of ~60-80 degrees to the lightsource are affected).
As those stability and optic issues don't appear under Dead Space, CoD4/CoD6, Left4Dead2, Silent Hunter IV, Stalker, Team Fortress 2, Dirt2 and Eve i won't accept an "AMD driver bug" as statement, as this simply isn't true (but it's easier to implement a workaround into the GPU driver than changing the game engine)
I solved my crash problem with my 4870 512 mb, how Verulam said a page before!
After flashing my GPU, no more crashs occurs while playing STO!!!
Shadow, check your Productkey from your grafic card and flash your GPU, if they're similar.
It's a long shot but is your 4870 a Sapphire card by any chance? My old Sapphire Radeon 4870 512MB had the same issue with certain games and at the time I put it down to Vista drivers (as with XP it was better behaved). I eventually found out though that the earlier Sapphire 512MB units had an older BIOS that caused the card to crash the system when it tried to dynamically adujst it's core GPU speeds.
The page I found that explained the issue and the workaround/fix is here: