There are a lot of good tips in every post here. I especially like that "cutting through" and "sitting in" were pointed out as being two very different things. I've also never been able to take part in the front-of-house world, so information from that side of things is very useful to me. Ultimately, I personally find it humorous that every review or question pertaining to any electric bass is answered with the ubiquitous "it cuts through the mix really well."
During my formative years as a bass player (early 90's), my local shops were overflowing with 70's and 80's rigs, and they were in my price range, so that's what I used. A lot of Sunn and Peavey, a few solid state Ampegs, some Trace Elliot heads, older Kustom rigs - stuff that was considered worn out and disposable that some people seem to be tracking down now. The one thing that the majority of them had in common was a sort of generic tone that blended in well. They all had their flavors, but ultimately they were loud, somewhat gritty, and somewhat flat sounding, but in a good way. Even mid scooped, a lot of them still had mid range presence that meshed really well with everything (except the Trace's - for some reason those always sounded really scooped to me, even when they were set flat). When we would get together to jam, we all just kind of cranked up and played - I'll be the first to admit that I didn't know jack about EQ settings back then - overall, though, we'd trade gear now and then and try to get the same sound on stage that we had in our rehearsal space, which was packed full of couches, and the walls were carpeted.
Moving on to the point here - back then, everyone in the band was young and starving for attention from the fairer sex, so we all played loud and tried to make ourselves heard and a bunch of individuals, rather than a band - we'd try to "cut through the mix" as it were. Since then, my wild oats have been sown, and I like to think that I've matured as a musician. I don't bring my 8x10 to coffee house gigs anymore. Rather, I try to write bass lines that keep a heartbeat with the drums and give the guitar player something to stand on. I want to stay underneath and out of sight, but I also want the sound to seem empty without me - otherwise, what's my purpose in the band?