Your girlfriend is attractive, kind and interesting, otherwise you probably would not have chosen to be in a relationship with her. But what you find endearing about your girlfriend, others are likely to as well. This is a fact of life. Other men are going to be interested in your girlfriend, just as other women are going to be interested in you. It doesn't have to mean the end of the world. With some healthy coping skills you can retain your dignity as well as your cool when uncomfortable situations arise.
Talk about it. Be open and communicative about new people in her life. Admit any jealousies or suspicions you may have about men she knows, however unfounded you might think they are. Hiding your feelings for fear of appearing paranoid or controlling will only hurt both of you when they come out passively or burst to the surface unexpectedly during the company picnic. You might say, "So I noticed you've been having lunch with Barry quite a lot. You're a beautiful woman and I just wondered if you've told him about us." You can also ask her to be honest about any feelings she may have for other men. As long as you take responsibility for your feelings and do not use blaming, accusing or threatening language, she should be receptive to your concerns.
Trust her. You can't control the fact that other guys are going to be interested in your girlfriend. You can't control what other guys will say and do to your girlfriend. Instead, trust that your girlfriend can put up healthy boundaries with men in her life that clearly deflect unwanted sexual attention. Knowing that you can trust her to reject advances or flirtations from other men is all the assurance you should need.
Hold her accountable. If your girlfriend is inviting or allowing flirtatious or otherwise inappropriate sexual or romantic attention from other men in her life, it is up to her to acknowledge this and to develop healthier boundaries. As much as you might want to confront her co-worker, fellow classmate or guy friend who seems to be transgressing the "friend zone," this is not your responsibility. If your girlfriend cannot assert healthy boundaries with other people in her life, then the aforementioned trust is null and void -- and without trust, there is no fertile ground for a relationship.
Examine your own self-esteem. If your girlfriend has proven that she can hold her own against male attention and has given you no reason not to trust her, but you are still uncomfortable with the amount of male interest she draws, the problem may lie in your self-worth. Perhaps you are secretly afraid that she will leave you for one of the guys at the gym, or someone better looking, wealthier or more intelligent; you're fearing that perhaps you don't measure up. Your lack of self-worth is not her fault. Instead of blaming her, do things to boost your own self-esteem: read self-help books, get into therapy, join a support group or develop a particular hobby or talent.