Sub on spikes?

If you have a front-firing sub or a dipole sub, you should definitely use spikes. And if your floor is carpeted, they should go through the carpet to the solid floor underneath. This is because the cabinet wants to move in the opposite direction of the woofer, and if it can, even a little, the bass will sound muddy.

If it's a down-firing sub and it's sitting on a solid floor (and assuming the unit is heavy which it probably is) the cabinet can't really go anywhere (at least in theory) so spikes are somewhat optional. In my opinion, down-firing subs don't give their best performance on carpeted floors, but if necessary, then use spikes that go through the carpet -- you don't want the cabinet bouncing up and down on the carpet+pad!

Some manufacturers, like Martin Logan in their Depth and Descent models, position multiple woofers in the cabinet so their combined reactive motions cancel out. Spikes optional.

Try both ways. I have a Strata III myself, and I prefer the spikes.

Spikes have traditionally been used to provide stability in tower speakers on heavy carpet, and also allow the speaker to be plumb and leveled on uneven floors. (the HF polar response could certainly be effected if the drivers are not perfectly vertical)
An unstable 4' 100lb tower is an accident waiting to happen.
MY B&W CDM 9NTs are extremely easy to tip over without spikes.

My subwoofer came with a set of large, scary spikes, but it's far too heavy to move once they are installed. (you'd have to pick it up and drop it, rather than sliding it; not easy with a big cube weighing close to 100lbs)
They're not needed anyway; there's no way this thing is going to tip over and it certainly is too squat to "look crooked".
One potential benefit of spikes; they prevent large heavy subs from making permanent dents in the carpet pad. My sub sits on 2" brass feet and they definitely leave a lasting impression in the carpet.

There's no sonic benefit from the spikes per se, unless the bottom panel of your subwoofer is overly compliant and is activating a hollow wood floor beneath it, causing buzzing and resonances.
Spikes would help reduce the transfer of energy to the floor, (or at least limit it to a narrower range of frequencies) and would probably give you a cleaner, crisper mid-upper bass.
Rubber feet are far more effective than rigid spikes for subs on hard floors though. (towers require a rigid mounting system to be stable, so rubber feet are out)

Another option is to float your sub with some Aurio Pro's and add some weight (25lbs of #6 Lead Shot) on top. I did this with my Velodyne 18" and it hit harder and cleaner. Without spikes or anything was not defined.

You are in luck. Holfi's boss had just told me not to use spikes. A quick search on Internet got me this article.

http://www.hi-fi-accessories-1.com/ringmat-theory.htm