Subwoofers were created because lower frequencies need more power for the same volume. To get extremely low sounds to be audible, you have to push a lot more air. That means you either have to have a larger speaker (hence the popularity of 12" subs), or more power - and the lower the sound, the more power needed.
Sometimes, you hear a sub do seemingly amazing things despite being in a smaller box. By putting a larger amplifier on an 8" sub, you can get some very acceptable performance. But even then, you generally aren't getting the REALLY low sounds, like the rumble of a fire or the deepest part of an explosion. What you generally get is a very powerful emphasis on the low-but-not-ultralow sounds. In theory, you can make any speaker play low enough with enough power going into it, but in practicality, there are limits to what you can do.
Some people will point to a well-made 8" sub, like Def Tech's SuperCube, and say I don't know what I'm talking about. But those are the exception, not the rule, and you pay handsomely for them...and you still lack some of the ultralows, even with the SuperCube.
You will probably need to spend $250 or more to get what you want. I am very happy with the H100, which can be had for about $250. The subs listed by Yoyo are well reviewed and generally thought to be better than the H100, and I understand that Dayton now makes a 12" designed by Dr. Hsu that is supposed to be a great value in the $200-250 range as well. You can, of course, pay more and get even more performance, but your money is no longer buying more range or volume at that point...more of a tighter, "cleaner" sound.