The best I ever heard is Count V's Psychotic Reaction done by Tom Petty and the Heartbreakers......pretty kick ass version if ya ask me!! Thanx Tom! http://it.youtube.com/watch?v=pWoYEXJXErs
Hm... the closest thing to a psych song by a non-psych band is the song 'Music' by the UK band Kaleidoscope. Stereotypical flower-power psych-pop suddenly going way ahead of their time with one very harsh, dissonant song, full of reverb. Totally trippy.
Sunshade and The lobster from Fairport Convention (generally very nonpsych folk rock) are very pyschedelic. It's on their debut. Heavily recommended!
If you listen to their Tangerine Dream album,you'd see how Psyche ,Kaliedescope were.Dive into Yesterday is amazing.
To say the truth, the first song that has that 'psychy' feel to it is a very old tune called Stormy Weather......listen to it and be the judge