Finest subwoofer for music under $1,000?

VAndersteen 2WQ sells used for well under $1K.

Brand new ACI Force, well under $1K or IF you can find a used ACI Titan. Easily comparable and in some ways superior to REL.

Infinity Alpha 1200S sub. My friend is using this on his Canton monitors. This sub lists for like 750. It sounds great on music
It uses that Rabos technology which is an equalizer to make sure the sub blends in perfectly to the speakers. It uses a Ceramic alluminum 12 inch woofer and a 500 watt amp. Here's a pic of it. http://www.infinitysystems.com/homeaudio/images/products_large/ALPHA1200SBK.jpg

paradigm's new pw-2100 for $730 retail is very good...nice 10" driver w/ 400w amp.

Its a stretch but for around 1K(used-usually abot 1200.00) you can get a Martin Logan Depth. It integrates with 2 channel as good as I've ever heard,and for surround its incredible.

vmps -take a look

As suggested REL is unbeatable when it comes to music and seamless integration. REL matches with any speaker you have provided you hook them up to the power amp output with your speakers ( kind of biwire which on the sub is called hi level). You run your main speakers full range and get the sub to mate with it, which means no nasty crossover glitches or distortion is introduced in the signal chain.

Strata III is a sealead unit which is even easier to blend with the room and speakers. Strata II was ported. All the models above Strata are ported. If you have a small to medium room sealed is better.

A used REL strata 3 is quite good for that price. You might even get one of their larger models. RELs are very subtle ... to the point where I often can't tell that mine is doing anything until I turn it off and the music loses all depth. Integration is that good. Subtlety and integration are the keys with classical music.
You really need to tell us your main speakers and your room size, and whether you have a preamp output to which to connect the subwoofer in order for others to make other suggestions.