Lot of really good recs in this thread! I think the necessities and more artistic films have been covered a lot, so I'll go a little sillier.
"Singin' in the Rain" is one of my favorite movies and I think it still holds up (mostly due to it being a period piece). It's light-hearted and fun, but well acted and can be very clever at times. ...it also should never have worked since it's a jukebox musical intended to highlight one composer's songs, so the fact that it managed to work them in while still managing to be coherent and entertaining is pretty impressive.
A little less known but one I personally enjoy is "Arsenic and Old Lace". It's a direct adaptation from a play, so it drags a bit in the middle (where there would have been an intermission) but the beginning and end are so worth it. A surprisingly dark comedy for the time, and a lot of fun as long as you don't mind people making jokes regarding murder.