I've used Cubase, Nuendo, and Pro Tools extensively and figured this should be a pretty easy thing to do in Logic... dunno why it isn't working...
It IS an easy thing to do in Logic.
If it is an Apple Loop, you can't apply fades, as stated by Juhani, but if it is a compressed file like an MP3 or AAC it also cannot be faded. It needs to be an uncompressed AIFF or WAV.
If you're trying to fade compressed files or Apple Loops, go to the Audio Bin, select all of the files in question (you can do a bunch at one time, just highlight them all), and then select 'Copy/Convert files...' from the Audio File menu at the top of the Bin. Select AIFF as the file type, and tick the box that says 'Change file reference in Bin' and it should convert all of the audio files. Your clips and editing that you did in the Arrange window will remain the same, but now you will be able to fade them.
Select the fade tool, and click and drag across the intersection between the two clips. You can make the crossfade bigger or smaller by how far into each segment you drag.
Good Luck!