Is it like Mega Man in which if you beat later stages you get abilities and can go back and get to things in the beginning stages that seemed impossible?  Or is this game really that tricky, and the only tools you have are the jump, time, and the keys?

Each stage has different time manipulation and it's up to you to figure out how  to take advantage of the time manipulation so that you can solve the puzzles

There is no backtracking or unlockable abilities . Although keep in mind you can use certain puzzle pieces in certain sections as platforms, that's the one thing that really threw me off in Braid.

" There is no backtracking or unlockable abilities . Although keep in mind you can use certain puzzle pieces in certain sections as platforms, that's the one thing that really threw me off in Braid. "

There's no such thing in Braid, although you can come back to previous levels if you missed certain puzzle pieces.  
Each world has a different time manipulation mechanic. You only use one in each world. It's not like when you reach world 5 you can use the mechanics you used in the previous worlds. 
The game's difficulty relays on strategy more than on execution. Unlike SMB where you need to perfect your execution so you can complete the level, here you must think and try to decipher what is it you need to do so you can complete the level. 
Braid is also not about reaching the end of the level, but getting all the puzzle pieces. There's where the difficulty stands. 
Although it can be a difficult game and sometimes it may look like it is impossible, it's very satisfying when you finally do it. The implementation of the different mechanics is amazing and, really, there's nothing quite like it.

You have time and it never runs out. 
 
Go.

" There's no such thing in Braid, although you can come back to previous levels if you missed certain puzzle pieces.  Each world has a different time manipulation mechanic. You only use one in each world. It's not like when you reach world 5 you can use the mechanics you used in the previous worlds. The game's difficulty relays on strategy more than on execution. Unlike SMB where you need to perfect your execution so you can complete the level, here you must think and try to decipher what is it you need to do so you can complete the level. Braid is also not about reaching the end of the level, but getting all the puzzle pieces. There's where the difficulty stands. Although it can be a difficult game and sometimes it may look like it is impossible, it's very satisfying when you finally do it. The implementation of the different mechanics is amazing and, really, there's nothing quite like it. "

It seems like a lot of people are are missing what was largely the point of Braid: The story and he way it ties into the gameplay. The mechanics are mind-blowing but they aren't just thrown at you, there's a reason they're all there. Before each world there's a few small pieces of text which advance the story and the game mechanics act as metaphors for the emotions in the story.

It kicks you in the testicles and then stares you in the eyes to make sure you know how pretentious it is.

Maybe Braid is pretentious, but at least it's trying to expand the horizon, isn't that credit due? I don't want to sound like a jerk, but fact of matter is that no one is forcing you to play the game. If you don't want to try/investigate what this game has to offer, don't play it. That's why I don't play CODBLOPS, because I don't think I will find things that will interest me, however I must respect that other people like it.
If you go to something with shit-lenses on, then shit you will see. Personally I find Braid one of the most inspired things to happen to games in the last years. The idea of you being able to blaze through the levels, not completing the puzzles if you don't feel like it, is an expression towards the way we percieve games as something you by all means have to finish, and thus get your points for doing so, being able to tell the world that you actually completed the game. If, however, you want to meet some interesting thoughts and views of time, brougt into play, course and action, that asks you to play along and try to bend the rules of the game as mucn as you can, then you might just end up with some knowledge about the mechanics of time that you weren't previously aware of. That happened to me, anyway. So yes, essentially the only tools you have is time, jump and the keys, but the way I see it, the game is less about what actually happens on screen, than what you have to put your own mind into thinking. In some sense, I would actually contend that this game has the ability to educate you in the dynamics of time in a way you'd only be able to otherwise understand if you had a really vivid scientific foundation of a college degree or something like that. As for the story, there is somewhat of a beauty to the ambiguity of ot, because it appears everyone has their own opinion of what it means, which is excellent, because there never is ONE objective truth, there is only subjective perception.  To me the princess is not  a physical character, it's a term for human zeal and will. This will is reflected upon the player, who always wants to complete the goal, to achieve (greatness). But each time you reach your destined horizon, you want something more. Thus, the princess is not in the castle you thought, and you will never be able to be happy if you keep on putting your happiness on your horizon. I guess I could write an article about all this, I'll cut off now and just leave you with my recommendation of: 
If you want to find out why some people are all about this game, you kinda have to make an effort to "meet" it, by trying to go to the game in ways you're not used to in others. This is not a difficult task, it is just different.  
/rant

I still need to beat this game. Got stuck once and refuse to look up how to do it.