Where shoe covers. Wet socks are miserable.

Bring two spare tubes. Rain moves debris around which makes flats _much_ more likely during the rainy season, and you really don't want to deal with patching in the rain.

Expect to replace your rear derailleur shift housing loop more often - they gunk up in wet weather.

Chains which get wet need lubrication much more often, although I follow the same schedule I do in dry weather - wipe it off and add lube when it ceases to run silently.