Masks- masks serve to conceal a person's identity (d'uh.) If you're really serious about this a full face mask is the only thing that will do. This has a downside of possibly interfering with breathing and talking and if your super is going to an awards dinner in his honor he'll have a hard time getting sweet and sour shrimp past it. Mouth holes are just icky. Then again if you're really serious about not being outed the first and foremost rule is don't make scheduled appearances in public! Sadly these day even wet behind the ear cookie bandits have their own cel-phones so someone is going to take you picture and with the face recognition software on the market today only a full mask or similar covering will keep your identity private.
The other downside of masks is having some nut yank yours down over your eyes. You can minimize this risk by having lenses. These can protect your eyes as well as keep people from learning your eye color and race.
Half masks and domino masks don't conceal as well. But they are easier to hide. If you want to fight crime in street clothes with a mask you can whip one of these off and pocket it easily to blend in a crowd.
Interestingly the Lone Ranger wore a full mask in his earliest incarnation. It was switched to a half mask for the 50's television show. I often wonder what people thought about only his chin being sun tanned if he took his mask off for a night on the town. Then again it seems like he never took the mask off. He was always the Lone Ranger.
Masks can be part of a helmet for added protection. If you have a distinctive hairstyle or color you want to cover it. Batgirl, I'm thinking of you. Way to eliminate 97% of the possible Batgirl suspects because they don't have red hair. Of course wearing a wig as part of your costume is a great way to confuse your identity further. Yvonne Craig's Batgirl got that right. Mousy brunette by day, redheaded scourge of the underworld by night.
High tech heroes like to load their masks with all sorts of gadgets: voice synthesizers, polarized lenses, handless headsets, placebo detectors and such.
Makeup is a possible alternative, either in your civilian identity or super. KISS managed to keep their private lives private using heavy makeup for years. People might not twig to your two identities being the same person if one is painted blue all the time. Makeup can have a striking effect on a person's appearance (ask any woman) that can make two personas seem like totally different people.
Many pulp heroes fought evil in fairly ordinary outfit. By that I mean trench coats. Everyone owned a trench coat before 1950. Add a mask and presto, you're a mystery man. Not only do you cut down on custom tailoring but in a pinch the mask is removed and you are another face in the crowd.
Finally some super powers can hide your features. A speed demon who never holds still for a photo doesn't need a mask. If your powers involve illusion or shapeshifting all the above becomes moot. The only problem is if your powers stop working for some reason.