The Parent Trap begins with a really wonderful title sequence, which I think underscores just how great the magnitude of artistic talent was at Disney during the '50s and '60s, the period that I consider as the "Golden Age" for Disney. The Parent Trap is, of course, a live-action film. There is no animation involved, but it begins with an animated title sequence set to the titular song, The Parent Trap (written by the fantastic Sherman Brothers).
It's really very cute. The animations look like a mix of stop motion and paper-cut figures. The figures are really quite stunning. For the most part, they're only the roughest of caricatures. Actually, the only figures that resembles the corresponding actor is the woman, whose red curls are vaguely reminiscent of Maureen O'Hara. But for the most part, genders aside, the figures could be anyone.
To a modern audience, the title sequence serves two purposes. First, as it originally intended, it provides the audience with the basic background (a divorced couple with daughters, mischief, set-ups, etc). But on a more contemporary note, the figures have this very funny, unique '60s look. You can tell from the title sequence that this is an older picture, just from the style of animation used. The figures actually kind of remind me of the more vintage areas of Disneyland and Disney World- I'm thinking of "It's a Small World" in particular.
The scene is thanks to the talents of three men in particular: T. Hee, Bill Justice, and Xavier Atencio, all Disney legends who worked extensively for the studio, as far as I know. I have to say, they really did an excellent job. You finish watching the title sequence and you're all ready for a nice little, family-friendly romantic comedy. And if a title sequence can prepare for a film, it's done its duty. What more can you ask for?
NOTE: I've included most stills from the sequence (not all in chronological order) for you because I know it is not well documented on the internet.