Kenshin Himura - Probably one of Megumi's closest friends is Kenshin, who teaches her the value of her own life and rekindles her desire to help others. Though Megumi often flirts teasingly with him to irritate Kaoru, deep down she cares deeply for him and it hurts her greatly to watch him get hurt in battle.
Sanosuke Sagara - Though Kenshin offered Megumi the best advice she needed, it was Sano who dragged her out of Kanryuu's tower in his own brutish, cute way. Megumi and Sano have a strained relationship that balances between their irritation for each other and an affection for each other.
Kaoru Kamiya - It's sometimes hard to tell if these two are friends. If Megumi isn't trying to aggravate the heck out of Kaoru (which always works), she's practically slapping Kaoru around and accusing Kaoru of being a whiny child. However, Megumi seems view Kaoru as a younger sister of sorts, and often gives her well-meant advice, even if it's a bit rough.
Yahiko Myojin - Megumi and Yahiko have a friendly relationship. While he's young, he cares about her and makes a promise to her that he'll bring Kenshin home safely from Kyoto in the second season of the anime/manga, and he often travels with her around Tokyo to help her with her housecalls.
Aoshi Shinomori - These two don't start out as friends, because Aoshi had the task of keeping Megumi at Kanryuu's castle, but in the Revenge Arc they do team up to solve the case of Kaoru's death. So I figure if they can work together, they must get along somewhat.