Three games this time, GBA and GBC games.
First one had you controlling this warrior person with a house. But you didn't start with a weapon and were pretty much completely useless until you found a sword. You collected plates and brought it back to your house to regain HP, and there were some items you could carry. A ring that let you push blocks, a cross that blocked monsters from passing through when on the ground and made you immune to attacks and unable to attack (Though you could get stuck forever if you were surrounded).
It was semi-turn based, monsters would still move even if you didn't move, and movement was limited to one square at a time, and monsters could move diagonally though you couldn't. It was also a roguelike, death sent you back to the title screen and there was no way to save. I always failed repeatedly due to being only 8 at the time.
Second was this game where you played as a bouncing blob, you had to collect all the items on stage to advance. Some blocks would be destroyed if hit repeatedly, and some blocks were curved so you can only bounce in one direction. If you got stuck, you had to press A+B to suicide.
If it helps, the above were on an X-games in one cartridge that included Flipull, Tasmanian Devil, Hyperlode Runner, Volley Fire, Motorcross Maniacs, and some game where a penguin pushed an egg around; among others.
Last is a GBC game, you played as some guy with a really big hammer in a puzzle platformer thing. You had 3 hammers that you could choose from: The first hammer turned enemies into blocks and let you whack them to send them flying across the area until they hit an obstacle, the second just destroyed enemies and blocks, and the third annoyed enemies to make them follow you.
You used the hammers to traverse the levels, you could repeatedly hammer a ledge to climb it, hammer it into a wall to hold you there, or pogo on it to cross spikes. Oh, and it was set in a Japanese theme, with the bad guy being some greasy businessman with shades and a cigar who would attack you with giant robots at the end of each area. Assisted by a bald scientist with some weird symbol on his forehead.