Punch-Drunk Love - One of my personal favorite movies, it's just so surreal and bizarre. Adam Sandler is actually amazing in this.
Night of the Living Dead - This is an absolute classic horror title and started the whole Zombie movie genre that we are familiar with today. I prefer Dawn and Day of the Dead, but this is a very uncompromising, gritty film and has a really ####ed up ending too.
Raising Arizona - A pretty unique film for the Coens, their first outing on a dark comedy like this (I think) but it is goofy and cartoonish in all the right ways. Cage and Goodman shine in this.
Once Upon a Time in America - Heard a lot about this but haven't gotten to it yet.
Hot Fuzz - This movie is hilarious, sometimes I like it better than Shaun Of The Dead. Both films are classic although different in their own ways.
Groundhog Day - This became a huge pop culture classic. I remember when it came out and when I saw it. I always loved it, but it got more beloved over time, especially the past 10 years - maybe 20 though, not sure. There are some theories about it that explain the genius of the whole concept that I've read before. A seemingly simple, goofy slightly-sci-fi, slightly-rom-com comedy turned into a huge cult film like Big Lebowski. I'm okay with that status, probably one of my top 20 favorites or so somewhere.