Rode 90 minutes in a driving rain Friday. There was at least 3 ounces of water in my rear wheel. I had to remove the tire and tube overnight and let the water drip out through the Velox rimstrip and dry out. Front rim was dry.
Chain lube is a very personal thing (search the Forum and see for yourself), but Ice Wax doesn't lube at all when wet, but it's my regular lube. Most lubes that are good when wet are fine when dry, too, but they get your drivetrain all black and yucky. That's why they're good in the wet, they stay on the drivetrain, but collect gunk along the way. Wax based lubes will stop lubricating shortly after a soaking, subjecting your drivetrain to faster wear, but most of us have to make a choice - wax or petroleum-based lubes - as it's inconvenient to change lubes every day, or even every week. If you ride mostly when it's dry and rain rides are infrequent, then stay with a wax lube. If it's monsoon season, commit to a wet lube.
More important than lube choice is checking chain length and replacing your chain when it's wore out. Riding a chain beyond its time will kill your drivetrain faster than an unlubed drivetrain on the occaisional rain ride.