As an IT-service company we use several OSes. We use Freebsd on our internet servers, and Linux, Windows and OS X on desktop clients. I'm personally an OS X user since 10.1(Puma) and have never used Mac OS 9 (I have a strong unix background).
OS X's stability and upgrading smoothness is unmatched by either Windows or Linux! Only Freebsd is comparable.
We usually upgrade live servers with freebsd and clients with OS X immediately after release, and have never had any problems. (I mean any.) This is probably because we don't use any "special" applications, just common Apple products like iWork, iLife, and Omnigroup products, etc.
OS X (the system) runs immediately without any flaws. There can be some problems (as @boehj told above) with third party applications, but 95% of the applications usually work without problems, because developers build them in advance. You can already see applications that are Lion-ready.
So, if you are not a hardcore OS X user, ofc, you can wait a while "to make sure", but from my experience: it is enough check how your application run under Lion (by visitng the developer site) and if they are ok, simply upgrade & go. :) Forget the "windows service-pack" syndrome :).
As Kerri said above - ofc, backups are good. Not just when upgrading, but "just because". In 10 years I have never needed to restore anything because of an upgrade. Ofc, we restored when we moved from PPC->Intel and when switching to new Mac models, but never "just because the upgrade went wrong". I'm pretty sure that apple decided selling Lion ONLY as a download via the AppStore (without media) that the upgrade process would be well tested.