There are a number of common issues that prevent triggered emails from being sent. Most of these issues can be resolved by checking the following three things:
1) If you are sending a trigger on the date someone subscribes, make sure to set the time to 11:59PM or set the trigger to send to everyone who subscribed on the previous day. If you set a date based trigger to go out (example: On subscribe date at 3PM) nobody who meets the criteria after the send time will be mailed.
2) Make sure your trigger is being sent to the correct list. If the subscriber you want to mail are not on the list the trigger is set to send to they will not be mailed.
3) If you are using filters make sure the filter is setup correctly. If the filter removes all of the subscribers the trigger would have emailed, the email will not go out.