Typically, if you were looking for a subwoofer for under $200, I would say you would either have to build it yourself or settle for sub par performance. However, thanks to Parts Express and Dayton audio, you have 3 great options to choose from depending on both the level of bass and size you are looking for.
Subwoofers Under $200 with Great Bass
The Dayton SUB-80 is a small 8" subwoofer that features an 80 watt amplifier with a variable crossover and a frequency response of 40-180hz. While this one won't rattle your walls, the bass is quite full and will compliment a small home theater system quite nicely. The enclosure measures 11" W x 15" H x 14" D so it is very compact and perfect for a bedroom or any other small room. Perhaps the nicest thing is that this sub costs less than $100 and is by far better than anything you will find at that price range anywhere. Don't be fooled by other sub $100 woofers as many of them use 6.5" woofers and certainly do not come with a variable crossover. All in all a great little sub for those looking for a little extra bass and a low profile compact enclosure. More Info on the Dayton SUB-80 Home Theater Subwoofer
The Dayton SUB-100 is a great sounding little 10" Subwoofer that not only has good bass extension but comes in a compact size. The sub features a 10" long throw subwoofer with a frequency response of 30-180hz. It comes with a 125 watt amplifer and a built in variable crossover. The sub measures 14-3/4" W x 16-1/2" H x 15-3/4" D so it is compact enough to work as a dicrete low profile sub. This little sub is very affordable and you won't find anything that performs this well outside of Parts Express. All in all, a great subwoofer option if you want great bass with a compact sized enclosure.More Info on the Dayton SUB-100 Home Theater Subwoofer
The Dayton SUB-120 is a step above the SUB-100 in that you get a subwoofer that dips in the 25hz range yet still maintains the sub $200 price tag. This one is also a step above in size and power since it comes with a 150 watt amplifier. The sub measures 14-3/4" W x 17-5/8" H x 18" D so it is still relatively compact. This is by far one of the best values and you will be hard pressed at finding a sub that sounds this good for twice the price. More Info on the Dayton SUB-100 Home Theater Subwoofer