Are you talking SPS alerts  or WSS Alerts?
As far as WSS alerts go, you have to turn them on in the Virtual server  Settings
(of your virtual server) in Central Administration. There's several reasons why
they might not be working. Are the notification emails  being sent (if specified
to be sent) when you add a new user to a site? Are you receiving notifications
when you create  alerts, just not the alerts themselves?

Check that the sharepoint  Timer Service is running. I believe the account it is
running under needs access to the content database. Also check that your email
settings are correct. There are two places to check that, the default email
settings in Central Administration and the email settings  for the virtual server
under Virtual Server settings. Make sure you have a valid email address in the
From: field, I know it can't be a distribution group (it doesn't make sense to
have a distribution group in the From: field anyway, i know, but we tried it for
some strange reason...)

I get no email notifications when I create alerts  or when the alerts should be going off.

I do however get emails  when i set  up new users. I am going to get our server  admin to check the virtual server settings. Though I would think if the User emails are working, the email must be set up correctly on the server. I am thinking it must be this timer thing, which I assume is a service on the server right?

Take a look at the TimerLock table in your SQL tables for your content database and make sure your web  front end server  name is listed there. If not, edit the table to have your web front  end server name listed. I had the same problem last week. MS walked me through this resolution.

Server name was in there correctly and it still wont work.

I would definitely look at the timer service and the account
associated with it. I just remembered one other thing to look at. Virus
software (specifically McAfee) will block ports used to send mail, check out
this MS article -
support.microsoft.com/default.aspx

ok, the timer service is started and working  to its not that. i will look into the other two options.