Locke is both a friendly fellow and a major character, so it follows that he has made some bonds during the course of the game. However, one of the major problems I have with FFVI is that, because there are so many characters, they don't develop much of a relationship with each other. And, although we see that the group is very friendly with one another, we don't see much interaction, so I'm assuming that they develop their comraderie by fighting with eachother. Anyway, this section explores relationships with other characters in a strictly platonic fashion. The romance bit is in another section.
Terra Branford: Locke, of course, feels this pressing need to protect Terra, and for this he is willing to do anything. Locke's need to save Terra is what gives the story its start. Because Locke is near the first person she meets (and the first playable character) Terra trusts him. He constantly insists on going with her, out of duty. It's clear that he's willing to listen to her concerns about love and life, and he offers his advice and she takes it to heart, in her quest to find what in her life is worth fighting for. Locke will always be there for Terra, I think, even as his need to protect her and her need for protection both diminish.
Edgar Roni Figaro: Locke's best friend and confidant. Edgar is unique in that his two most important relationships were developed before the events that FFVI chronicles. Locke was Edgar's link to the Returner while Figaro was still technically an ally of the empire. The two developed a friendship, most likely due to their optimistic outlooks and similar determination to destroy the Empire. Both men are marked by a strong sense of duty, an outgoing demeanor, a love of women and a vibrant sense of humor. Locke's proud to know Edgar, as the young King of Figaro is worlds beyond Locke's current social sphere, and I'd hazard that Locke has quite a bit of respect for Edgar's title (and possibly titles in general.) I imagine their relationship has gone quite a deal beyond the personal, due to their obvious compatability as friends and the fact that Edgar knows of Locke's complicated past before the game's events.
Sabin Rene Figaro: These two don't have very much contact, as their plot lines don't seem to intersect anywhere. They're both upbeat, funny guys, although, Locke seems to have more of a purpose than Sabin, with less of the discipline. The one reference that Sabin makes to Locke is about a certain lust for "shiny things" and though Locke doesn't exactly take marks about his profession in stride, he probably doesn't mind the mockery otherwise. Still, I find it hard to conclude that their relationship is anything more than superficial.
Celes Chere: The iron maiden of FFVI, Celes is imperial in her demeanor and cold to even her allies. She is a fortress and the last thing she would want is saving. But we don't always want what we need, and Locke's simple desire resulting from life's complications forces him to save her from a soldier's death. To Celes this is beyond comprehension, and because of this action, she talks to him differently than to other characters. He is her gateway to humanity, so to speak, just as she renders him a real hero, and not just some shadowy figure from legends chasing away his past failures. In a way, I suppose, they both save each other, and there's a kinship in that, if it's a shade subtler than most friendships.
Shadow: Shadow and Locke could probably get along if they tried, because they have a lot in common, but I don't think that Shadow would let anyone get close to him, much less Locke, who probably reminds me too much of that painful former self. How he was when he used to believe in things. His quest is for redemption, and not for a reversal. As it stands, Locke's a bit uncomfortable around Shadow, Shadow probably prefers it that way.
Cyan Garramonde: Final Fantasy VI's other knight in shining armor, Cyan and Locke have so much and so little in common, it boggles the mind. Socially, they are in completely different places, spiritually, their so similar it hurts. But who wants to be reminded of their own tragedies? I could see a meaningful relationship forming somewhere down the line, definitely a deep and possibly mutual respect, but the differences in ages and in circumstance makes it hard to see a buddy-buddy thing happening.
Setzer Gabbiani: They don't get much interaction in the game, but I think that Locke and Setzer would get along great. Tragic love type past? Check. Looking for adventure? Check. Thinking that Celes is one hot mama? Check. It reads like a bad personal ad. Oh the places they'd go, oh the crazy drunken stories they'd probably come up with. It's a shame that Setzer doesn't have much game time, because I think he's awesome. I really think that there could be a real friendship between these two, beyond the comraderie in arms. This is in the "A friend will be there to bail you out of jail, a real friend will be sitting next to you saying, 'Damn, that was fun.'" kind of way.
Mog: Locke apprecitates Mog, because the Moogles save your but during the first major fight of the game. (Don't thank me, thank the moogles!) But yeah, Mog isn't really close to anyone, being a novelty character and all.