I wanted to get the ASUS AMD HD 7870 but that is out of my budget (I am from India and gaming products are more costly here). But I see that the price of the GTX 660 (non TI, 2 GB) has been lowered and its in my budget.
the 660 and 660ti are in a similar rank to the 7870, and this means they will yield similar results. so yes it will play the games on a full HD monitor however you will be playing at levels of medium with a possibility of high settings in some games.
It's plenty good for 1920x1080 monitors or less. The radeon r7 265, which is comparable to the 660, is supposedly coming out in a couple weeks and will be $40-$50 usd cheaper. I am interested in the same level of card and am waiting to see pricing on the 265 before I buy.