Analysis of either the franchise as a whole, or any of the individual movies.
Toy Story (1995)
Among the events that contributed to kicking off the main plot of the film, one of them involves Andy and his family needing to move to a new house. Another involved Andy's new toy Buzz Lightyear, which for the first time had Woody worried that he would no longer become Andy's favourite and thus losing his current position as leader of the toys. On every event where Andy is unwrapping gifts, the rest of the toys get worried whether or not they get replaced by new ones. On overall however, the first film merely teases on the Coming of Age Story, which would be further explored in...
Toy Story 2 (1999)
Woody is offered the chance to become part of Woody's Roundup memorabilia, which essentially means he had to choose between: 1) Going back to be Andy's toy and see Andy inevitably outgrow and leave him, or 2) becoming "immortalized" behind museum glass, untouched for eternity. The rest of the memorabilia tries to convince him on the latter option, with Jessie providing a Tear Jerker backstory about her previous owner Emily who eventually grew up and donated her to someone else. Woody decided to Take a Third Option by inviting the rest of the memorabilia to come with him to live with Andy, accepting that while Andy will one day no longer need him, he wants to cherish this relationship as long as it lasts.
Toy Story 3 (2010)
This film's major underlying theme is about moving on from the end of a relationship. The toys' fears about Andy outgrowing them have finally materialized. Andy wanted to bring Woody with him to college and plans to put the rest of the toys in the attic. A mishap made the toys believe that Andy is throwing them away instead, and they argue whether to return to stay in Andy's attic or moving on to find a new home. Lotso the villain of the film became who he is after he mentally snapped from seeing that his owner had abandoned and replaced him with a newer one. By the end of the film, Woody accepted that nothing lasts forever. Since Andy had moved on from playing with his childhood toys onto another phase of his life, Woody and the rest of the toys also moved on to find another owner who would play with them, making this a better alternative to staying untouched in Andy's attic.
Toy Story 4 (2019)
The (presumably) final film's theme is about letting go and making new choices. Bonnie, the new owner of the protagonist toy characters, loses interest in Woody. While Woody still shows Undying Loyalty to his owner, he increasingly gets questioned on it, especially when he reunites with Bo Beep who sees herself liberated as a "lost toy" without any owner. Gabby, the antagonist of the film seeks Woody's voice box to replace her damaged one, believing that Harmony would choose her if she became perfect. That did not work out, and Woody convinced Gabby that she has other options besides Harmony. In the finale, Woody himself realized he can and should move on from Bonnie. With Buzz's encouragement, Woody chooses to be with Bo Beep as "lost toys" instead, passing on the torch to Jessie as the new "Sheriff", and exchanging goodbyes with the rest of the toys - possibly forever separated.
The Life and "Death" of a ToySay what you will about the first movie (what with all those mutant toys and Uncanny Valley humans), but Toy Story 3 was the series' darkest installment. Many may dismiss the reason for this as solely because the third movie was aimed toward those that saw the original Toy Story in theaters fifteen years ago and grew up with the series - not only could the now-adolescent audience appreciate deeper themes such as abandonment and Character Development, but if the final installment in the series didn't exceed the standards set by the previous two, then it would be a grave disappointment for the audience. However, there is more to this than Sequel Escalation. This was more than a mere adventure for the toys - their life with Andy, and their life metaphorically, ends in this film. The entire movie was symbolic of the afterlife, and the choices the toys make determine their ultimate fate.
The Attic: Purgatory
When Sheriff Woody reminds the other toys that they still belong to Andy, he neither sugar-coats the facts nor suggests that Andy didn't want them anymore - he just tells it like it is. In a sense, Andy has "suspended judgement". Woody correctly says that Andy's not certain to have children, but it was a possibility. If not, however, the toys would most likely get thrown out after lord knows how long. So the attic is a standby phase of sorts, where the toys have ended their life with Andy and are now awaiting their fate. (Of course, the trials they go through in the movie are almost certainly a standby phase in and of themselves.)
The Butterfly Room: Heaven
Alternately, it's a cool and groovy retirement home. A place where they will be cared for, have many supportive toys to talk and attend to them, and perhaps exist indefinitely as they will get repaired because of these friends.
However, in the hands of the twisted monster, they are denied this afterlife, and instead end up in...
The Caterpillar Roomnote : Hell
A land where they are "tortured" by rough play, disfigured, and because the toddlers are so young, they can't really bond with any of them or any of the other toys. Survival is the name of the game, and a cruel leader keeps them against their will in this situation.
Tri-County Landfill: No Afterlife
The darkness and claustrophobia, the fire of the incinerator, Lotso's taunt of "Where's your kid now?note "... It's obvious what Pixar was symbolically invoking, but from another perspective, the dump is more like the concept of no life after death rather than Hell.
- Alternate Interpretation: Gehenna
Being Given To Another Child/The Reformed Day-Care: Reincarnation/New Heaven & Earth