NEW: CB500X. Frankly, I think it's uglier than a skinned iguana, but the local dealer talked me into riding one, and I was truly impressed. Light, nice balance between maneuverability and stability. Comfortable seat and ergonomics, relatively luxurious suspension for a price-point bike. Surprisingly good wind protection without buffeting my helmet. Optional ABS and panniers. At $6500 for the ABS version, it's a damn good value. I can ignore the looks now; this bike just plain works well, in nearly any environment.
Honorable Mention: My Can-Am Spyder RS-S, but I'm aware that this requires a looser definition of "bike" than a lot of people here are comfortable with.
OLD: Air-cooled, two-stroke, single-cylinder street bikes. I'm tempted to say Bultacos specifically, but really it's nearly all of 'em. I could try to explain, but Lane Campbell already did a pretty good job of it: "Bul Stories" by Lane Campbell.
WHY: A lot of bikes will make you grin the first time you ride them. A few will make you smile whenever you look at them, or for the first mile or two whenever you get on them. A few very special ones you never tire of; they keep you grinning no matter how long the ride is.
Actually I forgot the Ninja 650. It is fully modern without having limits so sky high no mere mortal can approach them. I also really like the look of the frame painted a contrasting color to the bike. If only that made one with a big round light up front I'd be all over it.
I like the first generation Yamaha FZ1 with the round tube frame as well. It just looks like I expect a motorcycle to look. Here are the wheels, here is where the fuel goes, here is the motor, here is the exhaust pipe...