What games do you play or want to be able to play? What settings?
What is the make and model of your power supply?
The GT 440 is not considered a very good value in a card. See this review:
http://www.techpowerup.com/reviews/ASUS/GeForce_GT_440/...
You can get much better performance for a little more money with the GTS 450, such as this EVGA card for only $100 after rebate and with free shipping:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Note that the review shows the GTS 450 outperforming the GT 440 by 74% on average.
If you don't want to spend that much, you can get an HD 5670 that outperforms the 440 by 10-20% and costs only $60 after rebate - this one the XFX comes with a lifetime warranty:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
You could go with a faster video card if budget allows. While it might start to be constrained by other parts of the system, depending on the game, it could still improve FPS by a fair amount for some games.
You still need to confirm that your PSU is large enough for the option you select.
When you can, you should also to increase the amount of memory you have. What operating system are you using and is it 64 or 32 bit?