I'd like to know if there are any cultural references to the series, or even have a complete list of them. Maybe there's already a wiki page for that, just haven't found it. I'm interested in art not related to gaming per se.

Anyway I'll share my findings.
1) The biggest is a funny-translated (to Russian) film "Lord Of The Rings: The Fellowship Of The Ring" done by Goblin. The Quake III related part (one of them?) is here.
That shit was BIG in RU internet when it came out.

2) There was an obscure Canadian progressive metal/fusion band Grey Matter. Some tracks of their sole 2001 year album are officially available here. Listen to Oyagaa, 6 minutes in it has 3 Quake III announces. One of the album booklet pages thanks Todd Hollenshead and ID Software:

3) There is another obscure Belorussian (boringly) avant-garde band Knyaz Mishkin. They have more than 20 years of history and also released an album in 2001, officially available here. Track 2 (really titled "Keen eye") features Quake I single player sounds in its middle and end.