How can I change which application is launched when I press the play button on my remote?

Some tool like Remote Buddy might help here, but it's probably much more than you asked for.

according to the writer : This seems to work with iTunes 8 and 9, although you'll need to redo the patch after upgrading.

Open a Terminal and type the following

cd /Applications/iTunes.app/Contents/MacOS
sudo mv iTunes iTunesX
sudo curl http://www.cs.umd.edu/~dmonner/iTunes -O
sudo chmod uog+x iTunes enter code here

From http://www.cs.umd.edu/~dmonner/iTunes

#!/usr/bin/env python

import sys, os, subprocess

launch = True
blocker = ""

apps = ["Spotify", "Songbird"]

ps = subprocess.Popen("/bin/ps -x", shell=True, stdout=subprocess.PIPE)

for line in ps.stdout.read().split("\n"):
    for app in apps:
        if app in line:
            launch = False
            blocker = app

ps.stdout.close()

if launch :
    os.spawnvp(os.P_WAIT, '/Applications/iTunes.app/Contents/MacOS/iTunesX', sys.argv)
else :
    print "Not launching iTunes while %s is running." % blocker

and you can read more here and here.