I just finished a unit on subliminal messages in music in my cognitive psychology class, so it's a topic that's very close to my heart right now!
People keep pointing out the Hotel California example... fact is, whenever you say "yes" followed by a consonant sound, it plays backwards something like "Satan." Try it in Audacity or some similar music editing program if you don't believe it. I didn't understand how that could work, so I recorded my own voice and all I can say is that it's true. Makes for a lot of music with subliminal messages about the devil, eh?? But going back to that specific example, more to the point....
"I was thinking to myself
This could be Heaven, this could be Hell,
Then she lit up a candle
And she showed me the way.
There were voices down the corridor,
Thought I heard them say...."
Reversed is....
"Yeah Satan, he organized,
Oh, he organized his own religion.
Yeah, when he knows she should,
How nice -- it was delicious,
He puts it in a vat, he fixes it
For his son which he gives away."
The question there is... what the heck could this possibly mean?? It means nothing! If The Eagles felt like putting Satanic messages in their music, odds are the messages would actually make sense. Why would they be subtle about their subliminal backmasking if they were willing to put what they put in the forwards version so explicitly?

That said, there are a few examples on that page where I think the artist probably did write the bidirectional lyrics with intention, and those are the Beatles songs about Paul being dead (because they put similar subliminal messages in multiple songs, on album covers, etc.) and the drug references in "Another One Bites the Dust" (mostly since the words aren't very clear in the forwards direction, which suggests they spent some time testing out different articulations to make it work).
What my psych professor told my class is that the supposed subliminal messages in music are an example of top-down mental processes, meaning that you have certain expectations when you listen to the song and your mind conforms to reconcile your expectations with the reality. When you hear the clip without seeing the words that you're supposed to hear spelled out in front of you (i.e., no conscious awareness that the sounds have meaning), the whole things sounds like a mess of gibberish. Only when you are shown what you're supposed to hear does your mind separate the gibberish into discrete bytes that actually make some sense in natural speech (English). So basically, since your brain wants to make sense of nonsense so badly, you wind up tricking yourself into hearing things that nobody (the artist, the devil, whoever you think is responsible) really intended to put there at all.
Well, it works for me, anyway!