Here are some of the common steam probs I have encountered and what I had to do to fix them:
Ticket Expired
Log out and exit Steam
Log back in again
Disconnected from Server - Client sent drop
Disable Cheating Death
Cannot get Steam to run/start updating
Logout and Exit steam
delete the "ClientRegistry.blob" file in your Steam folder (usually "C:\Program Files\Steam\")
Restart Steam.
Server Verification Failed
Steam is down
When prompted start in OFFLINE mode
Play as normal (server should let you join OK)