I stumbled across a fascinating analysis that attempts to identify the best film trilogies according to both IMDb voters and professional critics.
The conclusion is that IMDb voters rank the following trilogies as the best of all time:
Lord of the Rings
Star Wars (original 3)
The order changes if you only count the top 1000 voters, but those are still the top 5.
Astonishingly, but deservedly, professional critics (as collated by Rotten Tomatoes) rate none other than the Toy Story trilogy as the best of all time. Their top 5 includes most of the trilogies preferred by the plebs above, plus the Trois Couleurs trilogy.
It's a great article, with graphs and everything. Have a look!