For me the killer feature of AIM was P2P file transfer. Is there even a service today that does this? It was so easy to just click "send a file" and it worked fairly reliably. Dropbox comes close, but, of course, it is not a direct file transfer.
For something more in the vein of AIM, pretty sure Skype lets you send files too.
Edit: oops, I didn't know that Skype got rid of P2P, now files are uploaded to their servers
I can't say that I've used it, however.