(Props to 'funkyappledog' for pointing out this technique many years ago in this thread...)
In case you've been living in a cave for the past decade or so, Boards of Canada are two Scottish brothers who have forged one of the most interesting and identifiable sounds in electronic music in recent memory. Some have claimed the music reminds them of their childhood and the warped educational films they used to see in school. Personally, I always thought their music was the closest anyone had come to capturing an acid trip in audio form. Not that I would know anything about that. Ahem.
Part of the the fuzzy, psychedelic quality of their music comes from their process of recording instruments to old, beat up tape machines, which gives the music a warped, slightly seasick quality. As often happens in electronic music, people pretty much immediately latched onto this sound and wondered how they could reproduce it without having to forge in Grandpa's attic to track down a tape machine of their own. Fortunately, if you work in Logic, you already have a plug-in that will reproduce this effect quite readily: Tape Delay. Here's how you do it.
1. Call up the track you wish to warp and apply a Tape Delay to the insert.
2. In the upper lefthand corner of the Tape Delay window, make sure Sync is turned off, and adjust the Delay value to around 10ms.
3. In the Output section, turned the Dry level all the way down, and the Wet level all the way up so you are only getting the effected sound.
3. Adjust the LFO rate to taste (.54Hz works nicely). Push up the LFO depth as well (73% will do fine).
4. Now adjust your Flutter rate (something toward the low end) and Flutter Intensity to taste (try around 65%).
If you've done everything correctly, you should end up with something that sounds not unlike this little example I threw together quickly...