The animated series itself, which is basically showcasing his life God only knows how long before the imminent explosion of Melmac.
A more minor example, but in one episode ALF tries to become a magician. During one particular scene he reveals that one of his tricks is to saw Brian in half! Think about what could have happened to him (Brian) if Kate and Willie weren't there to intervene.
One episode has the Tanners go on vacation and the plane they're on stalls in flight. They're only saved because ALF figures out how to fly the plane. ALF wasn't supposed to be on the trip (he stowed away), but had he not been there, or had never even came into the Tanners' lives, they surely would have died there.
Trevor Ockmoneck is a fan of The Dodgers (as revealed in the second episode 'Strangers in the Night'). The show takes place in California and Trevor is from New York City (with a strong Brooklyn accent, to boot). The titular baseball team matches him perfectly (The Brooklyn Dodgers becoming the Los Angeles Dodgers). It makes sense that Trevor would be a fan of that team.
One might see Willie refusing to let Lynn keep the Ferrari ALF got her in "Baby You Can Drive My Car" as Willie being a wet blanket with a weak set of reasoning. However, there would have been better reasons for him to mention. First; The taxes would have been beyond what they could pay. Second; The car itself may have an extremely shady history; ALF bought it from a mysterious man with an alleged mango farm in Oxnard...which supposedly was swallowed up by an earthquake, leading to the guy fleeing to Paraguay note More likely the man was a con-artist, there was no mango farm and the car was stolen and palmed off to "suckers".
