I'm running the latest available on the repositorys Kopete version, namely 1.0.80 on KDE 4.6.0.

The issue is that I have have "Show tray icon" enabled but it doesn't show up...

Any ideas?

Have you checked in the hidden icon area?

Yes.

It isn't there. I have two computers, both running Kubuntu 10.10 with KDE 4.6, one of them it's 32bit and the other 64 bit. Both show the same behaviour.

Despite that, notification do appear, but if I want to access the main window, I have to run Kopete from ALT-F2...

It seems taht I'm not the only one... : https://bugs.launchpad.net/ubuntu/+sour ... bug/655646

It seems solved on the KDE 4.6.1 update...

I have the same issue with Kopete 1.2.3 on KDE 4.8.4 (Kubuntu 12.04 64bit).
Any idea how I can fix this?

Thanks,
Ron

Does the Kopete main window open?
If it does, select Settings > Configure Kopete > Behaviour > General. Make sure "Show system tray icon" is checked.