Even though you've said you don't want anything smaller than 600cc, I'd still like to second the EX500 vote.. Talk about bulletproof, and fast and agile enough to surprise anyone who doesn't expect that kinda juice from a twin.. I had one in the early '90s, and it was a rocketship.. With a Vance&Hines pipe and a jet kit, it looked and sounded good, would power wheelie in 1st gear, and would have me over the 1-ton mark without me really trying- honestly.. I'd get in the fast lane, get comfy, and then look down to find I was going over 100.. They are popular race bikes too, and plenty of them around- cheap.
The CBR600's are nice and very refined by now. They'll cost more, but have more power too. I love the look of the GSXR's, but I've not heard good things about the reliability (but I've never owned one, so I honestly don't know 1st hand).
Also, what about a Triumph? Either speed-triple or a Thruxton look interesting, are plenty fast, inexpensively priced, and supposed to be very reliable.
Jason