An argument/discussion, that's been had a few times. If you want to do stuff like video editing, definitely quad, or higher core, is better. For pure gaming it's a bit more complicated.
At the moment, few games use multiple cores, so for most games, i3 and better GPU would be better. There are exceptions. Some games, like BF3, benefit from quad-core, in multi-player role, when there are large numbers of players. A possible alternative approach MIGHT be AMD, where a quad core is cheaper, than Intel. Whilst each core performs less well, provided the saving means you can get a BETTER GPU, the gains, there, can make up for slight loss, in CPU performance, and it will be definitely better for stuff like BF3 MP, than i3. Also, you should consider that more games will tend to use multi-core, in the future.
If going for Intel and either GPU, 500w is adequate, although with the 7870, I might be tempted to use XFX 550 if that's available, at similar price. I would definitely go with the 550w if using AMD processor and AMD card.