Extended stored procedures are what I thought of first, too, and are probably the solution I'd use if I wanted to run the monitoring app on the SQL Server itself. But I'm guessing that's probably not the case.
I'd suggest using MSMQ as an intermediate layer, myself, since it comes with just about every version of Windows these days and is more or less tailor-made for this sort of thing. So, going through the layers, here, you have:
- UPDATE and INSERT triggers on your certain table, which call...
- ...a .NET assembly (added using CLR integration), which...
- ...puts a message describing the insert/update into an MSMQ queue on the server, which...
- ...is received by your tray app, wherever it's running...
- ...and then displayed.
There's sample code for accessing MSMQ from SQL Server here: http://www.codeproject.com/KB/database/SqlMSMQ.aspx