I've been a life-long fan of animation and recently have been reading the history/how-to/survey 'Animation: The Whole Story' by Howard Beckerman. The book discusses early stabs at animation, including J. Stewart Blackton's 'The Enchanted Drawing' and the jaw-droppingly racist (but that's how people were, we're assured) 'Lightning Sketches'.
Thanks to YouTube you can actually see 1900's 'The Enchanted Drawing' and marvel at how we got from there to the likes of 'Spirited Away'. It addresses universal themes like the joys of consuming alcohol.
Also on YouTube: 'The Humorous Phases of Funny Faces'
Neither of the aforementioned are quite what we think of as cartoons today, but rather film-enhanced versions of vaudeville-era 'chalk talks'. This 'Felix' cartoon from 1923 is considerably more sophisticated (and entertaining).
Unfortunately, I was unable to locate 'Gertie The Trained Dinosaur' (1914).