Mr. Freeze is one of the most surprisingly sympathetic villains in comic book history - all he really wanted to do was cure his wife of a seemingly incurable disease, until people screwed him over, resulting in him being forced to wear a sub-zero bodysuit and his wife being dead (to be fair, his original origin was a lot less sympathetic - he was basically just a crazy dude with an ice gun, which was more than enough motivation for the 50s). But Mr. Freeze's obsession with the loss of a loved one made him an interesting mirror-image to Batman, who you may have heard also has some issues with the death of family members. Also, he's way more interesting in the comics and animated TV series than Arnold Schwarzenegger's terrible ice-puns would have you believe.
If there's one way to really up the evil quotient of any given villain, it's "make them a big-time Nazi." In that regard, Red Skull has got pretty much every other villain beaten right out the gate. He's got a brand of evil that is a lot easier to understand by most people because his brand of evil was a real thing that sparked the biggest war in history, as opposed to most bad guys wanting to take over the world with some weird artifact or something. Which, of course, Red Skull has also been party to, in his quest for the Cosmic Cube. But maybe his greatest accomplishment (beyond his ability to never stay dead for long), was engineering the assassination of Captain America. Sure, that didn't last long either (technically he was never dead, just phased through space-time), but it's the effort that counts.
Not many villains' claim to fame is "being a huge math nerd," but Darkseid is something special. From the ominously-named planet Apokolips, Darkseid had something more than simple universal domination in mind: he wanted to control the will of all beings by solving the Anti-Life Equation. And instead of being bullied for his nerdy pursuits, he was widely feared for it. Also he was feared for - his superhuman strength, invulnerability, superpowers, and intellect (which he used most of all, typically manipulating others to do his dirty work for him). And in Final Crisis, he finally unleashed the notorious equation (through the internet!). The only (well, actually one of many) minor hitch in Darkseid's ultimate scheme was, of course, writing the word "freedom" on your face (in the language of New Genesis) negated the effects. So remember to write stuff on your face before opening that email attachment from the deposed prince of Nigeria next time, okay?
The Riddler should be one of the most successful villains ever - but his genius-level mind proves to be its own undoing. It's not enough that he pulls off a caper or whatever scheme he's cooked up - he has to leave clues, riddles, and hints for Batman. He wants everyone to know how smart and clever he is, how great he is at coming up with elaborate labyrinthian puzzles, and that wearing a green bowler hat with a question mark is a totally cool look and not at all stupid-looking. His skills are so great, he's one of the few to ever figure out Batman's secret identity on his own. The only problem is he can't tell anyone, because it would ruin the mystery of Batman to reveal it. Also, he forgot it, thanks to a blow to the head. Maybe wearing a helmet instead of a pointless bowler hat would've been the smart call, eh Riddler?
One of the great things about Batman villains is how they're often skewed reflections of Batman himself - the Riddler is Batman's detective skills, Two-Face plays upon his guilty conscience, Mr. Freeze on his grief over death, Poison Ivy his desire to have sex with green ladies covered in plants, and the Scarecrow reflects the very purpose of his "Batman" persona: fear. He took up the mantle of the bat to strike fear into criminals, the same fear they used against the citizenry of Gotham. But the Scarecrow, while never wholly great at actually accomplishing big plans or anything, was able to break the core of Batman by using his greatest fears and weaknesses against him. Also, he's great at keeping crows away from your crops, but never hangs out in cornfields to help out farmers. That's real villainy.