Hello... I've managed to play a few carts on Vice20, but only in the same way that you would on a real Vic. I've not found a way of autorunning the carts, but I may have missed something obvious! The following is useful knowledge anyway...
Basically, the Vic uses a number of memory banks for ram expansions and cartridges. Game carts usually occupy bank 5 (some use more than one bank and others have been modified to run elsewhere).
If you download cart images off the net, most of them will be set up to load automatically into bank 5. On a normal Vic20 you'd have to have a ram expansion to load the cart into (and you'd need a switchable one, like the official Commodore 8k expansion, to make it use bank 5) but I think Vice20 automatically has all expansion banks switched on anyway. I'll try and check this laters.
Once you got your favourite game's .prg file you load it in Vice20 in the same way you would launch a games on ViceX (or indeed any Xport emulator). The problem is it doesn't look like it has worked as when the game "runs" you just get the "READY" prompt. Relax - the game is there, you just need to reset the Vic.
Switch on the onscreen keyboard and enter "sys64802" (I think that's right) and press enter. Hey presto! Your game should appear... hopefully.
Hope this helps... if you want to run a game that loads into two banks, you have to load each block of the program seperately and then issue the sys command. I suggest that you save a state once you've got the game running!
More info (from real Vic20 experts!) can be found here:
http://sleepingelephant.com/denial/cheers