Monsoon Wedding. It's a nice transitional film with plenty of Hinglish but will warm you up to reading subtitles. It's not proper Bollywood in that it doesn't have any big dance numbers but it has cultural elements that will become all too familiar after a few films.
Kabhi Khushi Kabhie Gham is typical Bollywood fare in both its strengths and weaknesses. The music and costumes are fabulous. It has a strong cast but at times the story slows down unnecessarily and other moments are rife with silliness that probably weren't supposed to be silly. Nonetheless, it's one of the highest grossing Hindi films ever.

Since it was one of the first Hindi films I watched,
Dil Se will always be close to my heart. ;) Mani Ratnam is an amazing director. It's not typical Bollywood
industry fare but it is uniquely Indian. It combines star-crossed lovers, political intrigue and a great soundtrack. What's not to like?

A lot of people really like
Lagaan. It's a story that takes place during the British Raj so from a socio-historical perspective, it's an informative film. Also, if you don't know anything about cricket, you most assuredly will after watching.
Devdas did very well at the Cannes film festival when it premiered. The feel of the music, like much of the film, is the slightest bit dark but it's beautifully offset by the most fabulously ornate costuming and production design you've ever seen.

Another beautiful film with a fairy-tale like feel is
Paheli. It's only about two hours long (made with Western audiences in mind). It's an unusual film by any standard and visually stunning. One of my favorites.
Munnabhai M.M.B.S. The film is very silly--it
is a comedy--but it left me feeling warm and fuzzy at the end, no small feat, so it makes the cut.

Also, if you haven't seen
Bend It Like Beckham, you totally should. It's not Bollywood but it is Indian.