Plug in amp and suwfoorer to line conditioner?

Bottom line - Should I plug in my amp and subwoofer to my line conditioner? I have not bought a power conditioner yet, and I am trying to decide how many outlets I need.
As long as the conditioner has non-switched outlets for higher demand components like amps and such.
Unless your line conditioner is a Shunyata I wouldn't plug your amp into it. Shunyata's line conditioners are passive i.e. there are no active electronics used to clean the power. This means you won't lose dynamics or high frequency extension. With a passive cleaner you get the best of both worlds. Your amp gets full power from the wall and you get a blacker background, extended highs and more detail.

I had a monster power cleaner before I got my Shunyata Hydra 8, and even though I got a blacker background it really put a veil over my music. So if you are not going to get a Shunyata I would plug my amp into the wall. I don't think it will matter as much with your sub but some other members might disagree.
No, do not plug the amp into a conditioner unless you have a small amp.

Nrostov and DrrDiamon offer sound advice.

Amplifiers, even smaller current drawing ones, demand certain amounts of current for loud and/or complex musical passages. If anything else is on this same circuit/line, even a 40 watt light bulb, it can be just enough to choke the amp of the power it intermittently requires and can render the music somewhat flat and lifeless.

In my own case several years ago I had a 36 watt preamp on the same ciruit as my high current drawing amp. When I finally installed the preamp on its own dedicated circuit/line, the macro-dynamics soared even at lower listening volumes.

That being the case, one might imagine how a larger current-demanding component like a subwoofer may affect the musical presentation.

And as Nrostov pointed out, not just any line-conditioner should suffice. Many are not worth owning, and others still are active and draw their own current away from the amps.

I've been using the Foundation Research passive and dedicated line-conditioners for the last 5 years and last year I became a dealer and a dealer for them.

The older Foundation Research LC-2 had a current capability of 20 amps or peaks of 2600 watts which is more than enough for just about any amplifier(s). However, the newest and top-of-the-line LC-100 has a 100 amp current capability.

Theoretically, one could install one or two LC-100s to line condition an entire house although I would not try that.

Moreover, proper line conditioning affects many aspects of the sound across the frequency spectrum including a definite tightening up of the lower bass regions giving a more natural and well-defined bass so I would not discount the use of proper line conditioning there.