Sam and Frodo represent friendship between classes of people during hard times, and the hope that spawns out of that friendship. Sam is initially a servant to Frodo, but becomes far more as the story progresses. His dedication to Frodo is one of love between friends. He will do anything to ensure that Frodo reaches his goal, partly because he is Frodo's friend and partly because he has hope that there is a life waiting for him back in the Shire.

Sam is so upset in the scene where Gollum tricks Frodo into believing Sam ate all of their rations because Gollum's success signifies multiple things. Among them is the fact that Frodo is so out of it due to his burden, he has forgotten who he can trust and who he should trust. It also breaks Sam off from his only connection to his home.

Nothing that takes place between the two characters signifies anything about an illicit relationship. The only relationship in the entire trilogy that comes close is the relationship between Eowyn and Aragorn, but even then Aragorn remains true to stupid, stupid, stupid Arwen. I hate Arwen so much.