You'll need to provide some more information for someone to be able to guess
at what the cause might be, e.g. what version of Outlook are you using, is it
in an Exchange environment or not, do you have a delegate, do you have Rules
set up, etc.  You also need to be more specific about the problem, i.e. tell
us *exactly* what happens... with the problem items, do you see the
invitation but nothing in your calendar, or do you not see the invitation?

A lot of calendar problems sort themselves out if you follow the advice here
though:

http://office.microsoft.com/en-gb/help/HA011276781033.aspx