which follower is the most useful one?
I mean actually the more "useful" not the more powerful.
and which is the most annoying?

Dogs are the most annoying followers you could have. They get in your way, get you stuck in tight spaces and block your shots when using bows. As for the most "useful" followers, I'm not sure what you mean by it.

I think 'useful' is relative to why you have a follower, and what you use them for.

I've had Lydia tagging along since I got her, but after I hit the stage where money was no longer an issue I gave up having using her as a pack horse...but I do have her carry my bow, and a couple of specialist weapons for me, so I guess she is sort of my faithfull gun bearer. But I do have her around for company...crawling through dark draugr holes on my own is not my idea of fun...I like someone to cover the rear.

Regarding dogs though...yes, horrid. Always in the way and wandering off. I used Dogmeat religiously in Fallout, and was quite happy with his AI when I worked out how it operated...but not being able to have 'my' dog, and just having a stray hanging around that does it's own thing and gets in the way is irritating. Aside from that, these dogs look my the dog I had when I was a kid, and I wouldn't feel comfortable getting it dead.

The mercenary in Solitude is pretty flexible, a battlemage I think. He's in the wanking skeever.

Eola is the most useful and least annoying.

Well in that case, I guess the most useful follower for me is Aela, because she's adept at sneak and archery, and won't get caught so easily when I'm sneaking. If she does get caught, then she just acts as a decoy while I fire shots from behind undetected

Anneke Crag-Jumper is pretty useful. A good archer, doesn't jump in front of me as I launch a power attack, and can hold her own in melee. Can sneak a bit too.

I loled.

thanks to everybody.
Something is always annoying about the followers and that's about traveling. we have a horse but he/she should come on foot. is there anyway we can buy them a horse?

You can get nice followers from factions. For example, Cicero from the DB is great, good at Sneak and One-Handed. The Companions are good followers if you're looking for a warrior follower, and Brelyna at the College is a pretty nice Mage follower. I personally am using Mjoll the Lioness as my current follower. She's both a melee fighter and an archer, and seems to have a lot of health. Only problem is that she talks too much.
As for bad followers, there isn't really a "bad" follower. They're all good at what they do, some more or less. Dogs are pretty annoying, but if you don't mind your dog pushing you when you're standing still, find Barbas out of Falkreath and simply don't complete his quest. He'll follow you until you complete it, he's immortal and a pretty ok follower if you don't mind dogs' general behavior.

I think you can't. I tried making Mjoll ride a horse and she said that it couldn't be done.

On PS3/360, probably a housecarl that can marry like Jordis, but on PC it's whoever you want to mod.

I prefer to adventure alone, but sometimes I bring someone with me for RP purposes, and to carry my burdens.

One of my favorites is Uthgerd the Unbroken. The moment she said 'You don't know a woman until you share a strong drink and a fistfight with her', I shouted out loud 'You're sooo in!!!' I dismissed her however due to her impatience - she would wait only so long if you tell her to wait - one time I asked her to sit at the dining table at my house while I enchant a few rings, and after a short while she was up and told me she's going home. I didn't want to be screwed like that in a dungeon, so I had to dismiss her.

Currently I travel with Argis the Bulwark, and he's just that - a bulwark. Heavily buffed with health, health regen and various resistances enchantments, wearing no helmet because what's the point of those intimidating warpaints and scars on his face if they're covered with a helmet. I like the way he says 'I am sworn to carry your burdens', with no sarcasm and puns intended. He's the walking definition of housecarl.

Most annoying follower - Lydia, of course.

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Which follower?
- Witch follower
- peach follower
- rich follower
- B...ch follower

Kharjo seems to know when to use a bow and when to use a mace. He also sneaks when you do. You could do a lot worse.

Least useful, I reckon the East Empire woman. She's a psycopath. Use animal allegiance, then take out a healing spell and clairvoyance, she sees that as signal to attack the now allied animals. She also killed a wandering Bard, again because to her equipping a harmless spell means 'equip sword, kill anything in sight, friend or foe'.

I used Lydia until I tired of managing the inventory, didn't need to collect 'everything', and had plenty of coin. Now she just eats in the Whiterun house but never gets fat. Can't marry her because that item is broken and I've not been interested in or need to use any other followers now at level 38 and 209 in-game days passed. After stopping to use Lydia I still picked up everything and would review and dump 99.9% of it whenever Ratsneve became over burdened. Now I ignore opening barrels, but scan through everything else including any locked items and doors, but only pick up coin, lockpicks, torches, books (still for some unknown reason), potions except magicka--unless it too is a poison, and armor or weapons that improve what Ratsneve is using or are around 1,000 or higher in value. This means I can stay out of cities for a long time if need be and I like that.

I guess it varies with the character. I used Lydia, but she would tend to charge in.... Good mule though.

Now i use Aela - she is basically a match to my character. I've given her a great bow and a deadric arrow. She wears the Forsworn Armor of the Old Gods set, so she's easier on the eyes.

Followers should match or compliment your style - not mine.

Hope the suggestions give you some ideas.