Yes you can get a laptop that can run most of today's games ; some on low, but others on medium and high settings.
The best gaming laptop under $650 currently, would be the
Acer Aspire V5-573G-9491 .
This laptop has the :
> Intel Core i7-4500U which is good.
> NVIDIA® GeForce® GT 720M Graphics card which is a good medium level graphics card
>6 GB DDR3 which should do well with this laptop (can be upgraded to 8 GB easily)
>500 GB 5400 rpm Hard Drive
>6.5-hour battery life which is superb (you wont get the half of that from the average laptop)