I usually start at low level or level 1, but I've been happy with games I started at mid or even high-level.
It's strange that in all editions I have played, high level monsters/items/spells/class abilities just didn't get used. It makes me a little sad, to be honest. Sometimes, my gaming group looks at not-reaching-high-level as a failure, rather than the natural course of a campaign petering out or wrapping up.