I've started playing The Hanon Part I exercises in all keys, and it does seem to help my technique. I'm not trying for speed, just evenness and accuracy, and my hands seem much more "nimble," probably from playing deeper in the keys and because my fingers have to land securely on the black keys or jump over them to get to the next white key.

I also notice that my mind is more focused, since I'm transposing (in a very simple way).

Has anyone else found this helpful? Any downsides to this, aside from the fact that when I'm doing Hanon I'm not playing real music?

I find it useful. You are practicing technique, getting faster, and learning your scales really well that way.

From what ive heard many piano teachers teach the method of transposing Hanon and i think it could be helpful even though i played Hanon as it is written(without transpose).And it is also helpful from a theoretical point of view and for scales..so why not?

For me it's helpful. I learn how the different keys "feel". I noticed my fingers find their place more easily in the pieces I play. That certainly is an advantage of transposing Hanon.
Besides it's boring playing the exercises in C major only.

I think this is the best way to work the Hannon excercises. I was always taught that you can speed up the learning process if you incorporate multiple excercises within one. So, in this case, instead of just learning technique, you can learn the notes of another key at the same time and become familiar with how it feels under your fingers.

I also think it's very important to do it slowly at first as it sounds like you are doing. Playing it with a metronome so it is smooth and even before speeding up is key...

I've tried Hanon several times, but my hands just cramp up....obviously, there's a tension problem. How slow do your start out? I'd like to clean up my playing...make it more precise.

I would start as slow as 50 or 60 as the quarter note. If you are tensing up, be sure your entire upper body is relaxed, not just your arms and hands. Also, make sure you start with the first excercise before you move on so you don't overdo it...

I start at 50 and work up to 72. Since I'm going for accuracy and evenness, there's no point in going for speed at this point.

From The Wikipedia:
Both Sergei Rachmaninov and Josef Lhévinne claimed Hanon to be the secret of why the Russian piano school delivered an explosion of virtuosi in their time, for the Hanon exercises have been [required]for a long time throughout Russian conservatories; there were special examinations in which one had to know all exercises by heart to be played in all tonalities in highly advanced speed.

So we're in good company.

That's great. I really like the Hanon's but for a while I was getting a little bored with them. I think doing them in all keys is a good idea and I will start doing that.