Most of what I listen to doesn't fit the format of "songs", so I'll just list my favorite five pieces of anything that are each shorter than an arbitrary fifteen minutes. In no particular order, and picking only one per artist:
Glenn Branca, "The Ascension" (13:09)
Les Rallizes Denudes, "Enter the Mirror" (13:46 for my favorite recording, but most versions are a similar length)
The Velvet Underground, "I Heard Her Call My Name" (a quick 4:38)--"Sister Ray" is too long for this list at 17:27, but this track is just as good. The two of them are definitely my most favorite pieces by the band.
Merzbow, "Tokyo Times Ten" (11:08)--It was hard to pick one Merzbow track, and many run past fifteen minutes, but this one is off of the album Pulse Demon, one of my favorites.
Mono, "The Flames Beyond the Cold Mountain" (13:29)--Possibly my favorite Mono piece under fifteen minutes, but it's really a toss up among five pieces.