Like some others, I feel that I can get a usable tone out of any rig, as long as it provides enough volume to keep up with drummers, and #$%^!n' guitar players.
For my tastes I dislike:
Hartke Aluminum Cone Speaker Cabs - Not only do they sound tinny, they look tinny
Gallien Kreuger Microbass Combos - Farts more than a football team that gorged themselves on cabbage, chili, and White Castle Hamburgers
Carvin heads and cabs - The only thing that would make them sound more generic is to put a white label with black stencil lettering on them
Fender - though I hear their new stuff sounds better, the older stuff has no soul. They are the Michael Bolton of bass amps.
Ampeg Portabass Cabs - Nice concept and sleek look, but there's no booty whatsoever in these cabs. It's like taking Jimmy Walker's butt and putting it on J Lo. Yup it's that ugly.
But for practical purposes, a big factor that makes me rule out a certain cab or head is weight. I like heads that weigh around 25 lbs or less. I like cabs that weigh under 60 lbs. Needless to say I don't care for Mesa 400s, Ampeg SVTs, Ampeg Cabs, Trace Elliots, Eden 4x10s, etc. I like the tones, but hate hauling the stuff around.