If youre a beginner serious about improvement then stay away from bullet/blitz. If youre a class player serious about improvement, stay away from bullet/blitz. If youre a titled player, or just play chess for fun, then bullet/blitz is fine.
Is bullet chess bad or neutral (or good)?

Bullet & Hyberbullet are a video games versions of chess, the real chess is far away from what they are doing in bullet.

A strong case can be made for the value of blitz as a way to quickly investigate new openings; provided of course you carefully review each game. Bullet not so much. Pretty much useless except as a way for titled players to idle away free time and the idle to push wood.

If I'm going to watch and enjoy chess I will enjoy it more if:
1. The game is decided by who played better, i.e. won over the board, not the clock
2. No stupid blunders just because a player is very short of time. Stupid blunders like beginners ones.
3. That the game isn't either incredibly slow or incredibly fast
4. I'll generally prefer won-lost games over drawn ones, but there can occasionally be an entertaining draw.
If it's grandmaster chess then I'd probably take more of an interest in chess960 rather than seeing a load of moves following the book.

I hate bullet chess with a passion! I however see the the slight postive affect of improving your speed. but other than that i don't see anything other but negative things.
Many a game just ends - no resolution - just that one player moved faster than the other! Even worse than blitz - there is absolutely no chess involved here, it is played predominantly by bored teenagers.
Note on GM bullet chess: High rated players do dabble in this, mostly to improve their reflexes and show off their ability to finish the game in the time allotted. Most GMs could defeat an average club player even if they just had 1minute total for the whole game while the other player had say 40 minutes!
So you would expect that the majority of the players playing bullet chess to be great players -right? Wrong.
"I am a CM, and I have to tell you that this is all complete crap. First of all, any good player needs an opening base: if you make a mistake in your opening, you're screwed for the rest of the game. Also, bullet chess forces you to recall openings and their transposing mid-games, as well as help you develop strong endgame tactics, so you can checkmate quickly. Please stop being a stupid 800 ranked player and go back to the rest of your crappy life
For those of you who want to get good at chess, it takes time and practice, but it's not as hard as you believe: consistently use certain openings you like, that suit your playing style, learn how to deal with different endgames, and find the tactical motifs of chess that can occur in any game (knight on a file is generally worse than knight on c file)
Again, author of this article, you are stupid "
A comment from that page.

Bullet can improve your tactical alertness and test your opening knowledge and your intuition. It is only "bad" for your chess if you forget to slow down and think during regular time-control games.

For beginners, bullet will likely do more harm than good. At this point, there are still a ton of fundamentals that the beginner should be learning, and racing the clock isn't the best way to build that base of knowledge. Slow chess is probably the best format at this point.
For intermediate players, bullet might help hone one's tactical vision, but their positional play will likely suffer from the rush of things. At this point, blitz might be more beneficial than bullet, if one's interested in a bit of speed. At least with blitz, there's still some time to think ahead and consider the position a bit deeper.
For advanced players, bullet's a fast-paced way to hone and test the skills you've already developed. At this point, slow chess has already been mastered to some degree, so why not introduce some speed into the equation to make it even more fun and challenging? :D
In terms of improvement and chess ability.