Best GPU for me

[Exercitus Mors]

Whats the best GPU can my computer handle without up grading anything? Here are my specs:

Gateway FX6860-UR20P Desktop PC - Intel Core i7-2600 3.4GHz, 8GB DDR3, 1.5TB HDD, Nvidia Geforce GTX 550 ti

 

[Rammy]

Tricky question to answer without the right information. It'll be dependant on two factors, mainly your Power supply, but maybe also your motherboard. Another thing to consider would be the length of the card. Also a budget would be helpful.
All I could find from a google is that it's supposed to be an H67 motherboard and a 500W PSU.
Without knowing how good that PSU is, it's hard to make a good recommendation.

Assuming your 550ti works fine and uses one 6pin PCIe connector, you should be absolutely fine with a GTX660 or an HD7850. Anything above that is really dependant on how good your PSU is and how many connectors it has, as they will use two 6or8pin connectors.