I have a suggestion, lets all quit posting to this thread so the poster goes nuts. Hahahah, it seems he’s the only one in disagreement with us all, which was probably the reason for the thread, to argue etc. Best to leave this one alone, and not give the satisfaction.
Yeah, the shorts dont count for obvious reasons. but even if we’re talking about “spirt and intent” the 3 toy story movies are still a trilogy. just because they didnt have them in mind before starting each one doesnt make them any less connected.
Lets compars this to one of, if not the most famous trilogyt of all time, Star Wars.
This is from wiki, but they cite sources.
What do I take from this? George Lucas in fact didn’t plan it all out, and certainly didn’t plan for it to be a trilogy from the start. he merely had some scenes/ideas that he wasn’t able to use and when the time came he found a way to work them into the sequels. sound familiar? the guys at Pixar did the same exact thing here. they intended to have the Buzz Lightyear cartoon open the first movie, and for Woody’s nightmare sequence to happen in the first. they weren’t able to, so they used it in TS2.
They intended to introduce a teddy bear character in the first, they were able to use that in TS3. the list probably goes on.
if you don’t consider Toy Story to be a trilogy, then by your definition neither was Star Wars. if you dont think that was one, then your just plain nuts.
Bottom line, they might not have intended it to be a trilogy form the start, but they sure as heck did when all was said and done. There are no contradictions in these movies that suggest an alternate time line or anything and are obviously connected.
I didn’t just start this thread to disagree with people! But okay I’ll concede, Toy Story is a Trilogy 
Thanks to all who contributed