I've seen videos of Rpg Maker 2003 games, with these huge monsters on the map, even though you can only make small events and characters. How do you do that?

You either use multiple events or pictures to represent the monster.

Cherry released a big character patch for 2k/3, give it a go.

Only applies for rm2k from what I've read.
Also, using the patch effectively seems to be about as tricky as doing multiple events, since it's only the graphic which gets bigger, meaning that if you have a sprite covering 3x3 tiles, you can walk through all of those tiles except the middle one (or one of the other tiles) unless you do some eventing to prevent it being possible.