My favorites, in no particular order:
Mike Tobias 535-24. I remember Bass Player Magazine gave away one of these back in the late 1990's-- it had a Myrtle Burl top and a translucent green finish similar to the green hue shown above. I've always liked the shape of Mike's instruments-- giving a nod to the classic J-bass contours, while being very sleek and sexy! (Picture taken from the MTD Website.)
I think, of the symmetrical-waisted (non-offset) instruments out there, I have always liked the look of the Pedulla Thunderbass. Again, a slight nod to tradition, but thoroughly-modern at the same time. Knockout finishes and figured woods certainly don't hurt, either! (Picture taken from the M.V. Pedulla website)
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Which brings me to the next instrument- Carvin's ICON bass. It kind of looks like the love-child from a tryst between a Tobias and a Pedulla-- and the result is stunning in its own right! (Picture taken from the Carvin/Kiesel website)
And now for something completely different-- The angular, "Hi-Tec" look and construction of the basses by Status, U.K. This is a picture of their new "Series 3" model from their website.
Ultimately, my favorite bass is a Swamp-Ash-bodied P-bass with a maple fretboard, but there were already a whole bunch of P's and Ric's in this thread, so I thought I'd chime in with some of the more "modern" basses that have always "checked the box" for me.