"I'll get your vices back, Max, or kill us both trying!" "I love you, too."
"You're the best friend I ever had, Sam!"
"And you're mine, little buddy."
Sam & Max Beyond Space and Time
A slightly twisted one, but how much Sam misses Max when he's stuck in his own personal hell with Peepers as a partner at the end.
"You'll crack me up, future Max!"
"Don't I crack you up now, Sam?"
"It was a baaad day on the moon/and then a saaad day on the moon/and an okaaay daaay on the moon/when Max came yakking back to me..."
In the finale for "Chariots of the Dogs," when they're about to go through the Bermuda Triangle, Max helps pull Sam up and smooths down his tie for him. It's easy to miss little affectionate moments like that, but they're there.
Most of the truly adorable or heartwarming moments are incredibly easy to miss, since they're just slipped in like that. For instance; in "Ice Station Santa," when Sam and Max are trying to climb up the foliage to reach the chimney of Santa's workshop, Max keeps slipping down and finally just throws himself onto Sam's back.
This is actually a Fridge Logic example (I think), but if you read Sam's mind a few times in the beginning of "Beyond the Alley of the Dolls", one of the thoughts he has is something along the lines of, "Max is getting so powerful now, he probably won't need me any more..." However, Max does not seem to think so; he still follows Sam everywhere, and, like Sam says, he doesn't even need to. Now THAT'S friendship!
When talking to Little Sam and Max in "Chariots of the Dogs," they can't resist ribbing the younger versions of themselves; but Little Sam retorts that he doesn't need them, because he doesn't need anyone else but Max, who never makes fun of him.
"That's right! ...poindexter."
There's also the way Future Max looks after Future Sam, who's grown hopelessly senile from all his adventuring. Future Max doesn't show anything but compassion and understanding towards the old duffer.
In 202, when you inspect the punching bag in the office, a little back-and-forth ends with this:
Max: No way, Sam! I could never stop loving you!
It's a little less heartwarming in context; two lines ago Max had mentioned that violence was how he showed affection.