Resident Evil 2 has a moment where Leon catches up to Femme FataleAdaWong, and attempts to make conversation. Keep in mind Leon is wearing a blue police uniform with insignia everywhere and the giant letters R.P.D. emblazoned on his back.
Leon: "Ada, I don't think I've introduced myself yet. My name's Leon; I'm with the RPD."
Ada: *shrugs as if to say "Uhm...okay, thanks for sharing"*
Another funny moment is in the N64 version of the game. Rebecca has a report about Billy Coen being dead, but she mispells his name 'Koen.'
"Do you want me to take care of this for you, little boy?"
While Resident Evil Gaiden is... well, not a good game, and is ignored by the rest of the series, it does contain one golden moment of hilarity (hopefully intentional), when Leon is confronted by a bunch of Umbrella guards with MP5s.
Guards: "Get back! This is your only warning! Do not approach the submarine!"
Jump off a ladder (don't catch Ashley) and aim at her, or perform a suplex and land under Ashely, and she'll call you a pervert and cover up her skirt.
Made even better when Leon dies under her, she'll be calling pervert when it fades into "You died" screen.
In the island military base, there's an oven containing a Ganado. Most first-time players won't know what to do (and take double-damage if the fan-nicknamed "Oven Man" grabs them), but those expecting should step back immediately as soon as Oven Man bursts through. He dies of his own burns shortly.
Resident Evil Darkside Chronicles gives us this exchange between Leon and Krauser, stuck in a huge, flooding room with zombies, infected piranha and Hunter Gammas:
While Your Mileage May Vary on Quint and Keith, this troper actually preferred a slight bit of comic relief from the two, even during the "invisible Hunters" battle.
A particularly cringeworthy funny moment in Resident Evil 5: during the first battle with Wesker, he may at certain points suddenly shout "Your future HINGES upon this fight!" and then literally punch you through a door.
