This is because your Explorer shell has restarted itself and the affected programs didn't. They are still running, but the icon didn't get reloaded.
 
In Administrative Tools, go to Services. Hunt down the Service for the program that is having problems and restart it. The icon should pop back into the system tray.

Thanks OLEerror, but what if my application is not running as system service... It's just an usual application that I have run some time before the exploer crashed?

We need a little clarification here. Windows Explorer is one utility. Normally, it is used as a file manager, but it is really the power behind your desktop. In the Task Manager it is usually called explorer.exe.
Internet Explorer is your browser and sits in the Task Manager as IEXPLORE.EXE. If your Internet Explorer stops responding, clicking on IEXPLORE.EXE would end Internet Explorer and should have no effect on the icons in your task bar.

Sampson, I agree with you, but sometimes when I kill Intetner Explorer (IEXPLORE.EXE), all Explorer instances (including Taskbar) restarts too... And consecutively some of my System Tray Icons are gone...
Okay but it is not that important how Explorer craches, the point is that my Tasbar reloads and that's why my Tray Icons disappears... All I want is to bring those icons back without killing their processes in Task Manager and run those apps again...

It surprises me that it does that. Anyway, many of the programs that startup at boot up that are not in your Startup folder (or startup folder for all users) are found in the following Registry entry:
HKLM\Software\Microsoft\Windows\CurrentVersion\Run. (There used to be three or four places in 95 and 98 so it wouldn't surprise me if there weren't more in W2K.) Copy and paste these entries with their full parameters to Notepad.
 
Create a new folder from your Start Menu Programs and call it Task Restarts. Create shortcuts for each program you found in the registry. With the full path of the program plus the parameters you saved in Notepad, you should be able to fill in all you need in the shortcut you are creating to insure that it will be invoked correctly when you have to rerun it to bring back the icon.
 
If you don't like scrounging through the registry, there is a version of msconfig for W2k on the web. Or you could use System Mechanic (www.iolo.com) which has a Startup Manager and would find all those programs normally stuffed into the taskbar.
 
Its a kind of kludgy fix, but it should work.

I've found that the best way to fix this problem is to log off and log back on again. It only takes a moment, and everything will look like it did the last time you logged on.

Just FYI, this is fixed in XP... icons are restored automatically when (if ever) explorer must be restarted.

No it isn't fixed in XP. I lose tray icons when explorer crashes. It's very annoying when this happens, because you can't get your tray icons back unless you restart the application. I'll probably revert back to W2K next time I need to format or something. It's MUCH more stable imho.

I've never had explorer.exe crash. I've had programs stop responding and had to end their task in the Task Manager. If explorer.exe goes down, I would think it would be better to reboot since any process initialized at bootup remains in the security context of the initial bootup. Log back off and then on may not necessarily put those processes under control again

It's pretty good at recovering from a crash. I'm never forced to reboot, but I have lost icons on a few occasions. It rarely used to crash until I applied some MS hotfixes about a month ago. And it still takes a lot of stress to cause a crash. I couldn't tell you which hotfixes cause trouble, b/c I qchained all of them at once. Probably should've just waited for the service pack instead. But hey, that's part of the role of this computer, for experimentation, and to find out what things to avoid on the important machines!