First in my head:

The first movie that comes to mind is "Better off Dead".  It has a more well known spiritual successor "One Crazy Summer".  Both movies are hilarious if you like screwball humor.  The other cult movies from pre-internet days that come to mind were eventually discovered by a lot of people like The Princess Bride or The Big Lebowski.

Movies... hmm I think Stephen Spielberg’s War of the Worlds is underrated.
Also from him I think TinTin is underrated.
Super 8 is pretty good. I also liked an obscure Animal Planet documentary movie from 2003 called Alien Planet. I liked that a lot.

The recent Tomb Raider. Was a good movie with a good choice of actress Lara croft has NEVER been a sexy character,she's always been a strong female lead and a archeologist/adventurer. The movie seem to get slack for this but they had it all wrong.
The action scenes were intense and perfect for a movie taking off a video game. You could see yourself in them situation while playing Lara in the game.c
My only issue were the other characters (apart from the old women in the meeting room with lara as she obviously has a bigger part to play in future movies) were quite forgettable.

Looks like I got a lot of new movies on my watchlist

Holy s*** I didn't even know this one was panned by critics. How dare they. I loved that movie as a kid and still do.

Speed Racer (2007)
It still stands as the best anime live action Hollywood adaptation, and has some of the craziest visuals in any movie ever. As a childrens film, its campiness is welcome and it should've become a franchise.

Good call.  I love Speed Racer, but I remember it coming out about the same time as Iron Man, so it kind of got overlooked.

1. Shattered - with Tom Berenger and Bob Hoskins (1991). I loved the surprise ending and Hoskins character is great.

2. A Shock to the System (1990) - Michael Caine plays a devious office manager looking to quickly move up the corporate ladder.

I don´t know if these are underrated by critics, but they seem to be at least overlook by people.

Tideland (2005, a quirky movie directed by Terry Gilliam)
You Are My Sunshine ( 2005, South Korean melodrama directed by Park Jin-pyo)
Smiley Face (2007, high-art comedy directed by Gregg Araki)
The Triplets of Belleville (2003, animated film directed by Sylvain Chomet)
A Friend Is a Treasure/Who Finds a Friend Finds a Treasure (1981, horror movie directed by Sergio Corbucci)

I might have mentioned cube and cast away on the moon, but they were already mentioned.
Aaand I still managed to mention them again. They are good, both in their own way.