There are hundreds of user created levels - known variously as "mods", "total conversions" or simply "maps", all over the internet. When it comes to finding them though, many URLs are no longer valid, and it is easier to just google for a file name (perhaps adding "quake" as an extra search term) than to try and find the project's homepage - which is probably just dust in the ether now.
To run new maps, place the bsp file into the Quake/id1/maps subdirectory, and then start Quake with the +map MAPNAME option.
Installing mods is simply a matter of creating a subdirectory DIR and extracting the contents of the mod zipfile/tarball into this directory. The mod is started by using the -game DIR command line option.
For both maps and mods, all files should be in lowercase format.
QuakeTerminus has a good list of mods, and Tenfour numerous map reviews.
A few of my favourites are:
A modern mod which made my jaw drop, and has an equally impressive sequel, The Lost Chapters. http://kell.spawnpoint.org/convoked.html
Dark and bloody, with Doom's paranoiac atmosphere. A classic - zerstorer.zip
Hugely impressive mod only supported in Linux by LordHavoc's Darkplaces engine. http://www.planetquake.com/nehahra
Neil wrote the definitive Half-Life mod "They Hunger".
The quality and fun is in these maps too -
alba01.zip, alba02.zip, sofsp1.zip, sofsp2.zip, starshp2.zip
http://www.planethalflife.com/manke/
Incredible production values and one of my favourites -
oum.zip
Fat Controller's Oum page
Coagula is a six level compendium of maps originating from a contest. The novelty is that all maps are floating in the ether, and it's a great set.
The first level is tough. The game has some beautiful levels but plenty of raw edges - fantasy.zip
... is another medieval themed mod with great monsters and music. It's a little dated now, and the numerous spells can be overwhelming - bmfull.zip
SdS is a speed run through Mission Pack 1, Scourge of Armagon. Hilarious and amazing. http://www.planetquake.com/QdQ/sds.html
Cracking game-play and rivers of blood - czg07.zip
Fun with very innovative models, Ikka's plasma gun and the Doom cyberdemon - gibfact.zip
Little mods with great game-play! vigil.zip, museum.zip
Great models and quite innovative - navy3.zip
Scourge of Armagon by Ritual Entertainment (formerly known as Hipnotic Interactive).
Dissolution of Eternity by Rogue Entertainment.
- Both official mission packs are generally acknowledged as better than the original game.
Very original Quake total conversion, with the greatest (make believe) machine gun I've ever unleashed. Worth paying for.
Commercial mod now freely available: http://www.planetquake.com/impel
Xmen mod! Great Models. Shame about the game-play. ...When good mods turn bad.
One of the first commercial mods with nice monsters, but the game-play doesn't cut it anymore.
Well, can Quake get any better ? We humbly think so - Hexen II.
Raven software made this colourful adaption of the Quake engine, but the game was released with many rough edges. ...So beautiful, yet so cruel. And while it is not as widely distributed as Quake, the demo includes some of the games best levels and is available from the Sourceforge web site. Ozkan Sezer has plundered the open source world and added his own touches to bring Dan Olson's original Hexen II port screaming into the antarctic sunshine!
http://uhexen2.sourceforge.net
Another first for Quake was the implementation of it's own game language - Quake C. This lets mods work seamlessly on any operating system.
It is possible to install many of the editors which are used to make Quake maps, but creating full scale mods is real voodoo and beyond my knowledge. The only currently maintained world editor I know of is GtkRadiant.
QuakeForge include Quake C tools with their tarball, and the Quake Wiki has some relevant links for the windows platforms.