From what I understand, most people hate Daedra because of their actions or those of their followers. Dagon's followers destroy places; Molag Bal's spreads strife and disorder; Boethiah's followers commit murder, treason, rebellion; Clavicus twists your words and often makes each deal painful; Hircine only appreciates the strong and crafty; Namira's spheres are revolting; and Vaernima creates nightmares. The other Princes are less "evil" about their actions. Course they can still be quite painful to deal with at times. Azura for instance seems like a nice god to worship, but she doesn't really care all that much about her followers, only that they accomplish her plans. Sheogorath is well, insane. and Sanguine is indulgence incarnate. Mora is also somewhat "evil", not really caring about mortal lives.

Of course, I'll reiterate what the others have said in that the Daedric Princes aren't really good or evil. They're like people. When Molag Bal enslaves a soul, he doesn't know (or at least feels) that it's evil, just that it benefits him. Same even for Meridia, she doesn't care why you practice necromancy, she'll kill you anyway. Remember that she didn't start "life" as a Daedra, she was cast away from her "family".

EDIT: Oh and by "most" I mean the Empire at large; Khajiit and Dunmer revere certain Daedra.

I'm a lore noob, so I'm not sure if I'm completely correct.

I just know that i'm a Nord and i worship Talor, the mighty Talos !

Thalmor go to hell, Talos will always be worshipped in Skyrim.

Shor. Tell Akatosh to [censored] off. Always taking Shor's due credit.

Also supposedly Mehunes Dagon Use to be against destruction and was cursed to be the lord of destruction by Alduin.

They don't run the world, they ARE the world.
They sacrificed portions of their physical being to create Nirn. When you walk on Nirn you're walking on an Aedra, when you kill a deer, you're killing (in a very loose sense) an Aedra.
Everything you see and interact with on Nirn IS PART OF AN AEDRA.

Most description of Coldharbour (his realm) suggests it is a http://tvtropes.org/pmwiki/pmwiki.php/Main/DarkWorld, basically if Tamriel was drawn by Hieronymous Basch.

Aedra represent stasis. They gave parts of themselves to create Nirn, so if you destroy Nirn you can technically destroy the Aedra.

Daedra are Padomaic; they are forces of change. Not all Daedra are made of the same essence though.

Meridia for example is a wayward daughter of Magnus, and Malacath is a metamorphosed Trinimac.

Also I don't see Azura as evil. None of the Daedra are fully good or evil. Azura reminds me a lot of the Greek pantheon. They were capable of both benevolence, charity, and love but also pride, wrath, and jealousy. It's simply unfair to call Azura completely evil. On the continuum of good and bad, she's farther to the good side than Molag Bal though.

As for Sheogorath, he's the madness of Akatosh made animate when Akatosh killed Lorkhan (part of himself).

The closest approximation for Youkai we have in western culture is the fair folk, who we cannot understand.

And also, what about the other deities that don't exactly fit the pattern like Ebonarm or Malacath?

There are stories where the Daedra receive credit for some good. Even the mean ones. The Pocket Guide is pretty funny, in this case. They credit the Divines, and then they credit the Princes backwards. (All praise LAB GALOM, etc). Seems the best way to pray to the meaner ones is "hope they don't find you too interesting."