Crashes, locking up your console, save files get bloated and your game suffers. These work better on 360 and PC, and Oblivion has more DLC on the other platforms too iirc, I can't remember about the other games though. I have all the Beth games for 360 and they work fine, you see the odd glitch and maybe the game would freeze rarely but they work ok no matter how large your save file gets. The games were designed for PC and had to be dumbed down for consoles, and the PS3 suffers because of its design (memory in particular).
Edit:
The Souls games are probably worth a look. They can be tough and involve grinding but are very addictive. I do recommend you do some reading as the games themselves come with virtually no instructions that are of any use gameplay wiseI also recommend you start with Demon's Souls, it's cheap on Euro PS+ atm but dunno how much it is on NA.