Long Ago . . . Wait, Wrong Movie
Naturally the game couldn't stick completely to the movie plots. Not only would there be no surprises for anyone but the six people who haven't seen the movies, but each of the three would require a whole game to itself--or more. So the game condenses the plots of the movies somewhat, taking the six most important elements (or at least six somewhat important elements) from each movie. The best bits are all present, from the rolling boulder and gun-verses-sword scenes from Raiders to the Zeppelin of Last Crusade (OK, so I'm a big sucker for airships).
Some of the characters get more active roles in the game than they had in the movie--Willie's role in Temple of Doom goes from helpless damsel in distress to LEGO baddie ass-kicking chick who is actually necessary to the resolution of the story, for example. And Sallah gets to do a whole lot more than he ever did on the big screen.
Each time you get through a level, you open it up for "Free Play" which allows you to go back as any character you have so far unlocked. If you want to collect all the items and get a 100% completion, you'll need to go back through all the levels, probably more than once. You can also build your own character out of assorted LEGO people parts, and play through with that.
Tiny Indy . . . Really Tiny
Different characters also have different weaknesses, which can affect their ability to perform. The female characters are afraid of spiders, while Indy himself can't stand snakes.
All this makes for one really fun game (though some of the environments do have an odd lack of actual LEGO pieces in their makeup). It's not without its flaws, however. The first and most noticeable problem--and this holds no matter what game system you're playing on (except maybe Nintendo DS, which is a whole different game anyway)--is the camera. You have no control at all over the camera, so you can't look around or adjust your view to better see a jump or dangerous obstacle. It's frustrating, but tolerable. I have seen very few games with really good camera systems.
Buried . . . Or Obvious . . . Treasure
So, while LEGO Indiana Jones: The Original Adventures is a great game and very much recommended, if you have a game system other than the PSP (there are versions for PS3, PS2, Xbox 360, Wii and Windows; the DS version is really a different game), you might want to consider playing it on that instead. If all you have is a PSP, I don't think you'll regret buying the game--just be prepared for a lot of squinting at tiny objects.