Personally I like the 5-string Fender Jazz Bass (http://www.fender.com/products/search.php?partno=0136600332). The slightly wider neck just seems to make it look better proportioned to me. Maybe I’ve just got used to it.
Heres a seconding of the Es-175
That guitar is a part of me…if only I looked as good as it does. 
I have one, and I love it (I’m going to get a set of flatwounds for it, too.) The stock white pickguards on Fender Jazz basses look horrible, IMO. I took mine off and played without for a while, then made my own pickguard from wood and put a brown finish on it. It looks a lot better. (The bass has a sunburst finish.)
I like the Rickenbacker Bass, like Geddy Lee used to play early in his career. It looks like its about 9 feet long. Very cool.
I have a Yamaha BB300 in Pearl White with stickers all over it. If it was in perfect tune, I might be able to play 3 notes. 
But no love for the the bodyless Steinberger? 
I really like the look of my baby, which is a slightly translucent black Spector legend bass that looks like a more subtle version of this.
The ESP Eclipse has always, always been my favorite.
There’s a particular artist signature model that just… wow. I’d rather have it with the EMG 81/85 pickups instead of a strat layout, but either way…
http://www.espguitars.co.jp/gallery/sugizo/python/index.html
http://www.guitarsatbmusic.com.au/esp/readersrigs/andy_s-1_python.htm
There’s also the Brilliant guitar, which was made by burning aluminum sheet metal prior to cutting…
http://www.espguitars.co.jp/gallery/sugizo/s1bmm/index_e.html
The particular bass is probably the most famous individual bass in the history of rock & roll! Funny thing is that he bought it in Germany because it was inexpensive - he couldn’t afford a Fender at the time. Nowadays I can buy a Fender for ~$600, and a Hofner Violin Bass will run me about $1800. All because McCartney played one.
My favorite? MTD Basses. No doubt about it. This guy makes the best, most beautiful instruments.
I’m also a big fan of the look of Matt Pulcinella’s basses.
I second the Gibson Explorer. I’ve wanted one ever since I was a teen and had a poster of Aerosmith with Joe Perry playing one.
I also like my Carvin AE-185 a lot. Kind of a telecaster-y shape but more stylish.
I’m torn between my loyalty to Mountain (Felix Pappalardi & Leslie West) and Rush.
The Gibson Les Paul Junior played by West during most of his early career certainly has a look that says function and art to it.
And Pappalardi’s Gibson EB-1 is certainly the coolest of the cool. Except for Geddy Lee’s Rickenbacker 4003. I’m so torn…
btw, I think on a Nirvana Unplugged video, Cobain (?) used one that was similar to the EB-1. I could be mistaken, but it looks EXACTLY like one that I used to have, with a real violin-shaped head on it. Does anybody know what kind it was?
Mine was an Apollo.
I only play at guitar, but I’d love to have an ‘antique white’ (sort of a pale yellow) Fender Stratocaster with a rosewood fretboard and a white pick guard like Roy Buchanan played.