Hi and welcome to the forum.
You're leaving out a lot of information here, it's difficult for us to figure out the problem if we don't know what email service you're using (hotmail, gmail, aol, outlook express, windows live, Outlook, etc), what Operating system you have, or when your links stopped working and what has changed since.
However, this happened to a few people that I know and it was usually caused by the default browser being removed. Windows didn't know what browser to open links in after that.
If you're on a windows machine, try going to control panel, open Internet Options, click on the "Programs" tab, and click the button that says, "Make Default", then click ok and exit out.
When you click a link, it should open Internet Explorer and display the link. If not, you can try holding the CTRL key down when you click the link (but that all depends on what you're viewing your emails with, which you didn't specify).