Once you have dressed for the rain, you have only two issues to confront: traction and vision. Traction seems to be the primary concern for most riders, usually because they aren't sure how much grip they have available. While some surfaces--metal fixtures such as manhole covers and bridge gratings, painted areas, and places where built-up oil and grease have not washed off--become much slipperier when wet, you can actually call on a surprising amount of traction on clean asphalt or concrete.
How much? The easiest way to test traction is to feel for it with your rear brake. Assuming you know how much deceleration you can develop on dry pavement before the rear tire breaks loose, you have a gauge of what's available if you repeat the test when the road is wet. This also assumes that you have a reasonable amount (say 3/16 of an inch) of tread depth. If you do this at moderate speeds on a flat, straight road, it won't become a thrill ride. Avoid locking up the rear wheel on a steeply crowned road, where it will tend to slide downhill and out of line.
During my ride to work on rainy days, I deliberately lock up the rear wheel two or three times as I come to stops. Once you have a feel for traction, you should have some idea of how much you can safely ask the tires to deliver under braking and cornering.
Some situations should be confronted with extreme caution. Railroad tracks can bite you hard when they are wet. The standard advice is to try to cross railroad or other metal tracks at a right angle, even in the dry. When they are wet, this is imperative. Otherwise, you risk having the tire slip into the groove alongside the track, which will immediately ruin your whole day. Other large metal road surfaces or metal sections running parallel to your direction of travel -- some expansion joints, for example -- are equally hazardous and should be approached cautiously and upright. A thin strip of metal can usually be crossed while leaned over mildly; tires slip then catch again after crossing. However, a large metal surface such as a bridge grate, a manhole cover or a cattle guard, may permit the tire to slip too much to recover traction. Painted surfaces can be almost as slippery as metal.
Places where the oil doesn't get washed away by rian falling on it can be thrilling. Watch out for surfaces where water gets carried in but doesn't fall on the road with the force or in the quantity to remove the oil. Toll booths and parking garages offer a chance to experience this sort of low-traction excitement. There is a highway tunnel not far from my house that's 200 or 300 yards long. The oil in there makes it feel a bit slippery when it's dry. When it rains, the surface is like buttered Teflon. Because the tunnel curves, it's a potentially deadly spot for motorcyclists, especially one who rides in expecting a momentary relief from the wet road.
Turning a motorcycle on such a slick surface demands an ultra-smooth approach. Getting on the brakes abruptly or making a sudden steering input could put you in the guardrail. So you want to be slowed down before you go in there and keep the throttle neutral all the way through --and be ready for cars that might get unstuck and block the whole mess.
That smooth approach to speed and direction changes will serve you well on all wet roads. Initiate your turns a bit more gradually. Downshift smoothly, engaging the clutch a bit slower than usual, and avoid abrupt throttle changes. Get on the throttle progressively. Use a taller gear to reduce the forces reaching the rear tire. Apply the brakes in such a way that the tires are not loaded abruptly. Allow more space to stop or slow down so that you need less. And also make sure that drivers around you have time to react to your moves.
Riding in the rain is OK. It's the clean up afterwards I don't care for