I have a character in 4e that I've been using for a while, but I recently met a DM who wants me and a friend to play his 3.5e campaign, since he doesn't like 4e or something... but our characters are 4e ones created with the character builder on D&D Insider.
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Short answer: Yes, you can, but it's not really any easier than starting from the ground up and building a new character.
Long answer: While fourth editon D&D shares many setting conceits with 3.5 and earlier editions, the two are very different games in terms of how characters are constructed and the way challenges are addressed during play.
You might want to check out this question about the differences between the two games for a general overview. The accepted answer is pretty good.
So, about converting your character to 3.5... Well, it depends on exactly what you've built, but since 3.5rd and 4th edition make reasonably similar assumptions about setting, it shouldn't be too hard to convert your character's concept across.
However, as you may have noticed, there are a lot of differences between 4th edition and 3.5, most notably including different scales of leveling and a differing level of combat-centric-ness that will likely make it impossible to convert your character without making compromises.
As far as I know, there's no formal downgrade migration path available, so you'll have to do the conversion the old-fashioned way: Hit the 3.5 books and try to work out how your character would fit the system.
Unfortunately, I can't give you more specific advice than that without knowing more about your character. Could you possibly post your character sheet?
Easily, but not simply.
Attributes: direct transfer
Class: pick closest class within classes available in the books you've got. It's a guessing game....
Skills: you've several in 4E; buy up the closest skill set (usually 2-4 skills in 3.X) to your 4E skill.
Powers: Some become spells, others feats. You'll have to make a case by case adjustment.
Odds are, you'll wind up with extra spells to pick (Keeping in mind most arcane spell-casters get 2 spells every level), and quite possibly short a few skill points in fighters, but with extra feats.
Gear: Pretty much, it translates straight across.
It is possible, under certain assumptions.
First of all, you should find out which classes you want to be. Single class is strong and balanced in 4e, not so more in 3.5e. Some character concepts translate well on 3.5e, several others don't.
Tanks do not exist in 3.5e, except for the reaaly bad feat Goad and a few prestige classes. Warriors and the like can be built as tanks in 3.5. Hard to hit, with loads of HP but since they deal no damage the monsters can just ignore them. The spiked chain warrior is the rough equivalent of a real tank because it stops enemies form getting near to the ranged strikers. A wizard with glitterdust, graese, solid fog could be considered a controller, the same wizard with blasting spells would be a striker but not a really effective one.
As for the abilities, 4e characters almost always work on a two attribute dependancy and this is supported by the rules for leveling. 3.5e characters work better if built on a single attribute but several classes require you multiple attribute dependency.
You should keep the feel and background of the character you'd like to convert, identify what it does in combat and how it behaves outside (is he a primal character? a marial? a divine?) and start from scratch.
Unless you detail me (us) your character and the books your new DM lets you use I can't help you more than this.