"Love is A Distraction" - He has a job to do and can't risk being distracted by something as petty as a love life.
"Love is Beneath Me," related to the above - he believes that to be someone the squad/city/world/universe can depend on, he or she has to be more powerful and more resolved than the average human and above the basest human instincts, especially if he or she is a Badass Normal. See also Love Is a Weakness.
He is maintaining a Secret Identity, and fears exposure if he or she gets too close to anyone. A Cape will frequently combine this reason with the "danger magnet" excuse, and settle for pining for their love interest from afar.
Rare today is the idea that the hero's powers rely on him or her remaining celibate, or that he is celibate out of religious or moral conviction. Most commonly this is found in fantasy settings, which may feature religious orders or mystical powers that may be influenced by sexual activity. Male examples, of course, are never in a setting based in the real world, because a man is never, ever a virgin, and don't you dare claim otherwise!
Rarely used in any notable works today in any media for reasons other than religious beliefs or medical disability. If for religious reasons, it is often depicted by bringing attention to the fact, usually in the form of temptation. Expect Buddhist (or any other celibate or abstinence associated religion) characters seeking to abstain from physical distractions to fit in here often.
Occasionally a case of a Hero everyone thinks is male actually being female, and pretending to be celibate, asexual or otherwise uninterested in physical relationships (and may be a case of panicking whenever touched at all for this very reason) in order to avoid discovery. You can pretty much guarantee that someone is going to try and pounce her anyway, and discover their true identity. If it's an ally, they'll probably be sworn to secrecy, but let it get out somehow anyway. If they're an enemy, you can be assured they'll use it against the Hero, especially if she continues to keep it a secret from her fellow teammates.