Mike,
Rig is far too generous a term for what I have chosen to plug my Alembic into over the years.
For more years than I care to count, I ran my basses through a Peavey TNT 65 solid-state combo. It was quiet, reliable, and utterly without soul. A fishwife's fingers possessed more warmth than this amp (and that's no exaggeration). I also had an assortment of cheesy foot pedals (chorus, overdrive, even a nasty 8-bit digital reverb).
When sanity and good taste finally gained the upper-hand, I upgraded to a Mesa/Boogie Buster 200 (1X15) combo. I find its sound to be very warm and pleasing and it finally revealed the tone of my Alembic in a way that my Peavey never, ever did. It's nothing fancy, but I like it a lot.
My latest guilty pleasure, however, is my Line 6 POD X3 (see my picture below). With its 28 bass amps, 22 bass cabs, and tons of pedals, delays, and mics, it's just a ton of fun to play with. The 8-channel, 24-bit, 96 Khz USB audio is awesome for recording and I can crank up everything in the headphones and never bother my wife who's sitting a mere 10 feet away. Are the amp models accurate? I don't know - I've never owned an early 70's Acoustic 360 or a 1968 Marshall Super Plexi. Regardless, having that many high-quality tones in one small case (authentic or not) is too tempting to pass up. (Heck, it even models the F-2B!)
Gord