Many Linux distros offer some type of upgrade path. The process varies from distro to distro (and sometimes release to release within a distro). The success you'll have depends on how much has changed in the new release. As long as you have everything backed up and you must move to the new release, you have nothing to lose by trying the upgrade path. If you run into problems, you can always do a fresh install of the new version.
I found this
nice little document on the
linuxmint site.
Fedora releases a new version every 6-7 months. Personally, I skip a version or two before upgrading to a new release and usually stick with the version I have until updates are no longer available. I'm on even numbers now. I always go ahead and do a fresh install (you can keep most of the custom configurations for your apps *home folder*, even though you have to install them fresh).
Some Linux distros are so called "rolling" distributions, which are continuously updated, with no release cycle. This approach has limitations, considering technology moves quickly in the Linux world. Sometimes, you just need to do a fresh install.