Executive Meddling: The studio wanted a PG-13 Alien Vs Predator film (the "unrated" DVD version ended up being basically the same movie save for several seconds of minor gore restored). This decision was later blamed on notorious Fox executive Tom Rothman. He was also alleged to have demanded present-day Earth be the setting instead of out in space in the future.
Given the name appears as such in the credits, "Grid" for the head Xenomorph in the first movie. The lead Predator is listed as "Scar".
Two from Aliens vs. Predator: Requiem...
The "cleaner" Predator was nicknamed "Wolf" - a reference to Harvey Keitel's similarly employed character in Pulp Fiction. The crew also called the Predalien "Chet" after Bill Paxton's character in Weird Science.
A very early script of the first film would have had the film take place in the same timespace as the Alien trilogy, complete with a Ripley expy!
Jerry Goldsmith and Alan Silvestri were planning to team up for the first film's score but Goldsmith's battle with cancer (and eventual passing) prevented the pairing from occurring. Which would have gone against his belief that there's no need for two composers working in the same film. He only needed an additional composer if he was pressed for time (as with Star Trek: The Motion Picture and Air Force One), and he couldn't make the deadline. "How many composers does it take to screw a light bulb?", indeed.
As mentioned on the main page, the Brothers Strause mention on the commentary that they had an idea of the ending where after handing off the Predator weapon to the military, the "rescuers" lifted up their weapons and the screen would cut to black with the sound of the rifles firing full-auto. Ouch.
Similarly, on the commentary, they mention that Colonel Stevens was originally supposed to be Garber from Predator 2, but talks with Adam Baldwin fell through.
Some of the script drafts toyed with the idea of Alexa getting on the ship and leaving with the Predators for the stars, which is the ending we all secretly wish they'd gone with.
Toilet Humour: Believe it or not, Aliens vs Predator was dreamed up when one of the creators, who was struggling to come up with ideas for a new comic book series, decided to take a bathroom break. During his break he realized that Fox owns both Alien and Predator franchises. He came running back to the room with all of his colleagues shouting "ALIEN VERSUS PREDATOR!" Yes, that's right; AvP is the result of a really good poop.note We can only assume Requiem was the end result of a really bad poop. *rim shot*