Brick: Why can't exceptional friendship, real, real, deep, deep friendship! between two men be respected as something clean and decent without being thought of as— Big Daddy: It can, it is, for God's sake. Brick: -Fairies...
A Year with Frog and Toad: Frog and Toad were always good friends in the original kids' books, but The Musical elevates them comfortably to life partners at the very least. They even invade each others dreams to sing about how much they like each other. Twice. ("That's funny, you've been in all my dreams too...")
Estragon and Vladimir from Waiting for Godot. They even have pet names for each other and put off killing themselves because of the slight possibility that one of them would live and be left alone. They were going to hang themselves so they could get erections. There is so much Ho Yay in this play, Wikipedia even has it's own entry on it.
Avenue Q: Rod and Nicky, who are CaptainErsatzes of Bert and Ernie respectively. "We live together, as close as people can get / We've been the best of buddies ever since the day we met!" Which segues, just a song later, into "If you were gay / That'd be okay / I mean, 'cause hey / I like you anyway / Because you see / If it were me / I would feel free to say / That I was gay / But I'm not gay."
MarkCohen and RogerDavis in RENT. Their duet, "What You Own" comes complete with Manly Tears and a big climatic Man Hug. The blink-and-you'll-miss-it instrumental reprise of "I Should Tell You" during their fight in "Goodbye Love" is also heartwarming.
Lucentio and Tranio from The Taming of the Shrew. Tranio is "as secret and as dear" to Lucentio "as Anna to the Queen of Carthage was"note Refers to Queeen Dido and her sister from Virgil's Aeneid, and he'll do anything to help Lucentio.
Enjolras and Grantaire from Les Misérables. This is somewhat more evident in the musical than in the book, probably because of how it's usually staged.
At least half the fandom can provide serious, significant, historical and textually-based evidence for their being canon-implied gay for each other (starting with the homsexuality coded via classical references to figures like Orestes and Pylades, heading into more explicitly canon territory with the book's acknowledging that Grantaire "loves" Enjolras, reaching a turning point when the two die as equals, with more or less HoYay-tastic dialogue depending on the translation, and then going off into fan-speculation based on interpretations of their motives throughout the text from there ...). It's the kind of thing you could write a serious academic paper, if not a thesis, on.
This was all made worse by the fact that the two characters were played by real life best friends, Ramin Karimloo and Hadley Fraser, in the 25th Anniversary Concert.
When all the other students walk off with their girlfriends at the end of "Do You Hear The People Sing", these two leave with their arms around each other.
Jason Forbach and Joseph Spieldenner, who play Enjolras and Grantaire, respectively, in the US 25th Anniversary production are engaged.