Any site to test how well games will run?

Can You Run It
But be cautious, it's very inaccurate. Only use it for a rough estimate.

Most sites can only give you a "ballpark" estimate.
Example: Assassin Creed IV recommends a quad core as a minimum. I run the game just fine with a core2 duo E8500 (2 core) 4 gigs of 1333 ram and a GTS 450 SC and get 45-60 FPS.

inb4 a certain moderator warns you about talking about illegal stuff in SGv2

To answer your question, though, Can You Run It can give you an approximation, but it's also quite inaccurate. If you're borderline, the only way to know for sure is to run it yourself.

I've found Game Debate to be good and quite accurate. It also has a rather large database of hardware complete with how well it performs compared to other hardware, and if something is missing you can request to have it added.

use the demo?

not all games have demo's though

Use Benchmarks.

Individual games have their own quirks. Hubby can run SR4 nearly maxed even tho he's right on the line, but EQ2 is laggy as hell even with much more modest posted requirements and fairly conservative settings.

Ask on gaming forums about particular titles.