I park inside and that's about all I do directly after my commute on rainy days... wipe down with a rag to dry it off a little. And even that I don't do every time. In fact, I used to do it more often than not. Now it's probably the other way around.
Other than that, I'd say keep an eye on the chain and the drivetrain. Rainy conditions and wet roads tend to make them dirty and need cleaning/lubing more often.
If you don't have fenders and your bike can take them, I'd strongly suggest you look into getting a good set.
It depends how often you ride in the rain but personally I'd rather not worry about having to do a lot of maintenance because the bike got wet. Put fenders on the bike to help keep grit out of places you don't want it. If you're worried about corrosion you can replace a lot of screws and cables on your bike with stainless steel versions.
Some people keep a separate bike for foul weather.
I wouldn't bother drying the frame off with a towel unless you needed to do it to bring the bike inside or something.
There's 2 things I've found I have to do after riding in the rain sometimes -
1. Add a little oil to the chain. Otherwise (though not always) it gets squeaky when riding.
2. Wipe down the rims on the wheels. With rim brakes, sometimes crud accumulates on the rims, then when you brake it gets noisy (and theoretically grinds any grit into the rim).
I'm not saying you really *need* to do these things, but if you have either of these problems (squeaky chain when riding, noisy brakes when stopping) these are the solutions. I don't even do them every time, just sometimes, and when I notice a problem.
Fenders might also reduce your need to do either item, though fenders aren't perfect either.