i'm not a big fan of 'remixes' but i like remakes. i like to hear different interpretations of the same music/lyrics. and cross-genre music is okay, depending on the artists/genres...

For me, it really depends. Example: Rabbit in the Moon remixes a lot of Sarah McLaughlin's work, and sometimes they hit (remix: Fear) and sometimes they miss (remix: Possession). Likewise, Paul Oakenfold does a lot of remixing of Madonna's songs -- but they're almost ALWAYS a hit, for me (whether this is because Madonna's got such great songs to begin with or because Oakenfold is a muffa genius, I'm not sure, but either way, I likes 'em).

I also tend to like it when artists remix their own songs -- Orbital has two perfect examples with Halcyon + On + On and Doctor Who (both of which are live remixes, which ruins them for me, slightly, on a personal level as I'm not a fan of live cuts).

Then there are the intra-genre remixes, where artists of the same or very similar genre remix another's songs -- like the Airscape remix of Chicane's Halcyon, to which I write a LOT of my code (though the original is the better cut, I like to mix it up by looping the two back-to-back).

I don't know if they count as remixes, per se, but I like a good number of mashups, too. There was a great Madonna/Daft Punk one called Da Funk Music and there's a fabulous one of Greenday/Oasis called Wonderwall Boulevard (which actually ends with a bit from Aerosmith's Dream On).

Just my thoughts.