Im finding it hard to disagree with LOTR. As Ken says though, Toy Story has to be up there. Back to the Future 1&2 are excellent I think, but 3 lets it down, as happens in so many cases. Id also have to mention the Bourne films as all 3 are excellent, but LOTR is in a different league.
Empire Mag did their own top33 trilogies you can see here
Just to be pedantic....
Are we talking trilogy - three films only, or film series/franchises?
If we're talking franchises (I hate that label, but what else can you call them?), Harry potter would have to be up there. Love it or hate it, can you think of any other series of 8 films (eventually) that has been so successful?
The alien films deserve a shout too (excluding the crossovers!)
Of course the original Indiana Jones trilogy should be mentioned too.
Another left-field suggestion might the the spaghetti westerns?
I'm just trying to think what had 3 good films..
I would have gone alien series but that's four films (I've got the quadrilogy)
matrix - got boring after first one
star wars is technically six films (yeah I know)
ringu has 3 films but they're japanese
honey I shrunk the kids
underworld (I quite like this series)
Ocean’s Eleven, Twelve and Thirteen are also not bad ... There is also The Terminator, but they made this fourth pile of s**t they have the nerve to call a movie ... Well, the third already was not really good ... Then there is Alien, but it also has four parts ... Third and fourth are better than Terminator 3 and 4, though ...