THIS POST APPLICABLE TO MT (MINI TOWER) FORM FACTOR ONLY.
Unfortunately no card that is more than 7.5 inches long or 2 slots wide will PHYSICALLY FIT inside the case - it was found that only single bracket video card can fit due to BTX MOBO, where card internals facing upward towards PC internals, not ATX, where dual card design is blocking another PCI slot by facing downward.
If you prefer the card with beefier fan, then the length of the card must not exceed 7.5 inches, otherwise only "skinny" single bracket, single slot cards can physically fit.
Pictures below will prove my point.
View shows no room for dual bracket
Single bracket only, or you have to cut dual bracket in half
Here you can clearly see only single place for the bracket
Visual explanation
7.5 inches explained, also shown "obstacles"
This is the picture of actual "skinny" single slot video card (not sure which model)- perfect, "glove" fit.
So, I found 2 GDDR5 7750 cards and one DDR3 4GB (GDDR5 is better than GDDR3, even if GDD3 offers 2 GB RAM or more), which confirmed in reviews to fit Optiplex gx620, 745 and 755 cases (the difference between those models are different processors).
Skinny, flimsier in terms of construction, completely single slot XFX 7750
http://www.amazon.com/XFX-DisplayPort-PCI-Express-FX775AZNP4-FX-775A-ZNP4/dp/B007Z3T5JC
A bit beefier cooler, not as skinny, more durable in construction PowerColor AX7750
http://www.amazon.com/PowerColor-AX7750-1GBD5-DH-Video-Graphics/dp/B00775OC28/ref=sr_1_1?ie=UTF8&qid=1362783129&sr=8-1&keywords=AX7750+1GBD5-DH
There are a few 7770 cards which will fit here as well, but they would require power supply upgrade as well, and this is the pain in Optiplex GX620 due to different positions for mounting screws.
Please respond to my first post about memory, Win and processor, this is CPUID link http://www.cpuid.com/softwares/cpu-z.html