Although there are entire books written on the subject, I’ll focus on the three keys to what I see as a successful campaign.
First off, it needs to actually play out fully, in other words, end properly. Too many campaigns are started and never finished, usually through no fault of anyone, it just works out that it never really ends and there’s no satisfying conclusion, which is really what constitutes a successful campaign to me. Running a campaign through to the end when you’re in high school and have lots of time to play is simple, but as you get older, it becomes a true challenge. As a result, my campaigns have gone from being completed in under a year to sometimes carrying over multiple years, with breaks in between.
Second, a successful campaign needs to be epic in some way. A meandering story which has no clear focus will be less fondly remembered. This is not to say that every scene the campaign needs to be epic, or even most of it. The sum of the campaign is where the epic should be found. It might be epic only in the lives of the characters surviving against incredible odds or it might be saving the world, but it needs to have major stakes at the end.
Finally, for a campaign to be truly successful, it needs to be memorable. If you’re not remembering well a campaign years later, it wasn’t truly successful. If it’s memorable, then a true story was told at the end of the day.
That’s my thoughts on successful campaigns.