Version:           1.9.7 (using KDE KDE 3.5.7)
Installed from:    Gentoo Packages
Compiler:          gcc-4.1.2 
OS:                Linux

When mail arrives and KMail runs in tray, it is marked as read even if it is not viewed by user. This behaviour causes problems especially, when mail list is empty. Then indication and count of new mails on systray icon don't work properly.

How to reproduce:
Run KMail, choose KMail setup (in settings menu). In your account menu select periodic mail downloading. In Miscellaneous select, that message should be marked as already read after some time. You may leave there zero for the timeout. In Appearance menu / Systray select that KMail icon should be ever in the systray. (The names of items in setup dialog may be different, I'm sorry, I haven't got KDE in English). You can also setup some sound on mail receive - only for your notification, cause icon in tray wouldn't work.
Now delete all messages and then send one to yourself. Close KMail window and wait for the mail.
If you've selected some timeout for marking the mail as already read, you will see in systray that you have one new mail. But after the timeout the number disappears, because KMail marked it as read. If you choose zero timeout, you'll not see any indication.