Mostly stuff from like 2005 or early. The Sims, Quake 4, WoW and Counter Strike would be good examples. With a lower end card like the 5470 you could play newer games, but you would have to really reduce the resolution and details. If you want an idea, find some of the games you play on here and see which cards meat your requirements: http://www.notebookcheck.net/Computer-Games-on-Laptop-Graphic-Cards.13849.0.html
Personally, I don't recommend the majority of HP laptops. The only exception to that is their Envy line. I have seen quite a few HP Pavilion notebooks die due to the same overheating issues. With Dell you'd need to look at either the Inspiron 15 or 17 laptops. Their GPUs aren't the best, but the studio line is more expensive then your budget (at least here).
Can you find Acer laptops? Acer has an AS7740G which comes with an i5 processor and an ATI HD 5650 for around 800, which is probably one of the best deals for the money.