I do this. I only have a couple of characters that I'm attached to enough to do it, but my favorite character, Majoru Oakheart has gotten continually remade(and ended up as my forum name). Even in 2e, I made Majoru in about 5 difference 2e games. I made a couple versions of him for 3e, one of which was his son. He was the first character I played in 4e.
Nope.
I "converted" a great (i.e. my favorite) character from 2nd ed to 3rd ed... a Specialty Priest of Leira (godess of lies and illusions).
I just didn't work. Since most of my characters tend to be detailed in both "fluff" and "crunch", I've found it painful to update them.
It really depends on how much emphasis you put on the small details of the mechanics of your character.
In 2e, Majoru used a Longsword and a Shortsword and was a half-elf Fighter/Rogue. He wore no armor at all because he found Bracers AC -2 (Yes, I know they don't exist in the books, our DM just kept making up broken magic items and giving them to us).
The key to Majoru was that he was swashbuckleresque. He was cocky, reckless, but lucky. The key to his character was that he had rogue skills but was still a good fighter...and that he used 2 weapons(longsword and dagger). Also, the reason he picked all of those things was because they powergamed him. I was given the character by one of the other members of our group because I was new to D&D and no one wanted to wait for me to make up a character.
When I remade him in 3e, I was really torn, since Half-Elves kind of sucked..and the idea was for him to be GOOD at two weapons and Rogue skills. His cockiness really doesn't work if he doesn't have the ability to back it up. I made him a half-elf anyways, and still had a good time playing him. The reason my character used a longsword and dagger in 2e is because he needed a smaller weapon in his second hand and longsword was the best weapon. However, I couldn't do that in 3e. So, he switched to 2 sword swords. No big deal. He ended up being a fighter/rogue.
In another game, I figured it was just better to play a character who was good with the same concept. In the original game, my character had married and had kids with a Drow. So, I played one of his kids, who had the stats of a Drow, even if he was only half. He ended up having some levels of PrC that gave him some powers he didn't really have in 2e. But it still fit the concept and was supposed to be his son anyways.
In 4e, he was a Ranger who multiclassed into Rogue. He had high Stength in 2e and 3e, because he needed it to be a good fighter. I figured that the core of his character was that he was a good fighter who used two weapons, so he needed to be a ranger. He took almost no Rogue powers. The more I looked at the list, the more I realized that the only thing "rogue-like" about him since the beginning was the ability to find and disable traps, and that he was dexterous and fast. Training in Thievery and Perception was enough to get most of that. Ranger powers were already dexterous and fast in their theme. He was able to use 2 Longsword due to his class feature, so he did. It was more effective than using anything else.
I'm not sure he really ended up as exactly the same character in any edition, but he felt the same to me. I guess if you based your character around certain very specific mechanics in 3e, it'd be hard to keep them intact.
My players loved it, even as they cursed at me.
