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.