For gaming the cards need to be linked and theres a limit, for simply desktop I'm not sure you're limited by anything other than pci-e slots.
Any bog standard 58xx series card will output to 3 screens though theres some limitations in that only two can be dvi, one (on most of them) have to be display port, meaning by a display port screen or get an active display port to dvi adaptor, though I believe theres cheaper dp to vga adaptors.
6xxx series cards, hell, to be honest I can't remember, 4 screens is more standard, easier outputs and adaptor compatibility, more dongles that make life easier with eyefinity special edition cards. For both series there are eyefinity 6 screen models.
For desktop only you can get one of the made 6 pci-e slot mobo's, put in 6 6450 cards and have a ridiculous number of screens, though for linking together in game/eyefinity there is a limit, but each can run basically independantly of each other running as many screens as they can.
I'm sure theres a limit somewhere, and it depends how much you play the stock market, crazy billionaire daytrader might want 20 screens each with dedicated stocks. I'm assuming 1-2 more screens would do you, simple option is display port monitors, any 5xxx/6xxx series card maybe get a specific 6 screen edition.
If you want gaming + more screens, Nvidia can do 2 per card, or surround(not sure if its more than 3 to be honest?) when using SLI, for desktop only I'm sure you can add a whole load of independant cards.
Basically if you can add display port screens your options are more open and numbers go higher more easily, if you're stuck on dvi, a couple cards would probably work best for you or a card that comes with display port to dvi dongles.