I ride in rain daily for much of the year in Portland. I am a big fan of tires that work well in the wet and for me these have been several sets of Avon Gripsters. I understand Avon tends to be generous with silica in their recipes and silica is good for durable wet / cold traction.
Regarding exploring available traction, it is very handy to have a good feel for what is available. My bike is a big single so it can strobe the rear tire out pretty easily on wet city corners. This slip - stick behaviour is very informative.
Watch out for wet front-wheel braking / slowing / turning across wet tracks, leaves, grates,... If you give the front wheel very little to do besides keep rolling when you cross these at shallow angles then it will usually work fine. Don't do anything on wet bridge grates and stay far enough behind whatever idiot is in front of you.
*Watch out for parking garages where the surfaces get wet but not clean. *Watch out for random auto oil drip weirdness. Some turns and streets seem to be atypically slick and you may get to know where these are so you can adjust. Paint stripes, painted bike boxes, and adhered striping can be very slick or it can be fine.
I too have unitentionally lifted the wheel in a downpour and it is not uncommon for the rear wheel to spin up a bit. I don't see alot of value to riding on wet grass with street tires.
Originally Posted by outlaws justice
When riding in the wet, explore available traction with the rear wheel primarily, and only with the bike straight upright. You can test the rear brake to its limit as well as perform acceleration tests to investigate the limits of wet traction you have (in a controlled environment of course). I was impressed one time when I was able to loft the front wheel in the wet, not that I was trying... but it's just a testament to the grip of good tires these days. Of course I have spun up the rear as well when assessing traction in the wet, but this is all part of the learning experience.