I can foresee many problems about this type of service...
1. The one that leaps out at me the most is that you're going to need a very good connection in order to do this. Of course that brings up the glaring question of "what if you don't?" And as someone mentioned before, how would you do multiplayer in your house? I doubt anyone would have the ability to run super-fast internet for 2, 3, 4+ people at once.
2. Games. What would get on it and would be dismissed? If the game isn't popular, then off it goes, if conventional business sense is used. And what if a company decides that they don't want OnLive to put their game on? What would happen to retro games?
3. And on the subject of games, let's think about the potential vulnerabilities of EVERYTHING being server side. What if the service goes down? Assuming the worst case scenario, you don't have any consoles to play games on, and no PC games either. What happens then? When would they do maintenance? Someone, somewhere would be playing games. Would they just shut them out for 3+ hours? There's something concrete about owning a game on a disc. It's a sense of security, of knowing you'll have the game to play if you want to. To me, OnLive doesn't promise that kind of security.
4. There's bound to be competition. If not from the big 3, then from someone who thinks "Hey! OnLive is a good idea, I think I'll do something like it." Then there's competition of who's games goes where, and then multiple OnLive systems being paid for, and it just racks up too much cost.
5. Can OnLive handle the stress of hundreds of users? As I said before, you need really good internet to do this. Can OnLive handle receiving all the inputs and sending them out? As I understand, they really haven't done massive stress tests yet...so can they theoretically handle WoW, Halo 3, COD, SCIV, SF, and other games?
6. What about portability? Say you want to bring this with you somewhere for single-player games, possibly multiplayer. What if your destination had no internet (this is a rare thing) or internet that wasn't fast enough (this is less rare)? What then?
As a serious gamer, I can't see this happening. There are way too many ways for this thing to go wrong, and a very very good chance that the big 3 won't let this thing be alive for more than a year.