No notification from my apps I have a strange behaviour on a HTC Desire Android 2.2 phone:

Some applications offer notifications that should appear in the notification bar and should make a sound - for example Seesmic (Twitter client) and Huddle (from Google+).

On one phone I have here for comparison that happens. Whenever I get a message on twitter or when I receive a huddle, the phone beeps and shows a little icon.

On the other identical phone, which to me seems to be identically configured neither of those applications give me a sound - although sounds are enabled in the applications.

Any suggestions where else I could have another look?

Since there is no sound from any of those apps, it seems to be a "global" problem, but I don't see where...
You could try:

Settings->Sound->Notification Ringtone

It has a Silent option which might be set.