My tonal goals are perhaps a bit different than what people might expect, given my playing style and genre of music covered. First off, regarding playing style, I am almost exclusively fingerstyle, and I generally play over the neck pickup (though, contrary to what others might think, my tonal objectives are far more clear and articulate than some might believe, given this proclivity for the neck pickup

). Genre-wise, I am currently playing mostly rock (hard, classic, modern, emo, you name it), blues, (some) pop, funk/disco (limited selections from both, and no fancy slap work!), (some) top 40, and some country. Though I have in the past also played jazz, bluegrass, small band and big band swing - and classical, but that is unamplified on upright, so that doesn't really count.
With this range of music, I tend to have a lot of different tones for different songs, and I like to bring a rig that can cover a lot of ground. But, my personal tone goals are very broad range, frequency-wise (think baby grand, but packing a punch

), fullness without muddiness, very balanced midrange (no big peaks/valleys), deep/full/
tight low end, great articulation from top to bottom, and a lot of definition to the attack. I also prefer SS roundwounds, and I like to get a bit of that 'finger scraping across the windings' kind of definition to the start of each note. I do like a very full tone (especially when I am playing in a one-guitar band), but not at the expense of definition and attack. Trust me, it can be a challenge (well, at least it used to be!) to achieve that mix of fullness/clarity/balance that I tend to go after.
To be honest, my goals for clarity/articulation are perhaps not entirely in line with the general expectations for some of the genres I play (which may tend to normally feature a more round, warm, pillowy tone that what I am getting - or at least going for). That said, if the song calls for it, I'll roll back some treble, play with the thick part of my finger, and get a nice big, warm, fat attack (without much zing). When I do the funk/disco stuff, it's normally the opposite - I dial in some high end and pluck in a more 'pop-like' fashion - though still over the neck pup.

I haven't really found anyone that sounds like what I am after in my head, though I do really like the sound that the bass player from Dishwalla gets on Pet Your Friends. And I love Timmy C, though no one can really cop his overdriven tones 100%.

I'm definitely more Steve Harris than Marcus (not that I can play like either, though!), but again, more clear/articulate than what some people might expect.
Tom.
P.S.
Sorry for the excessive verbosity. It's kinda what I do, though.