This is actually not how alignment is supposed to work in 3e, merely the simplest (and dumbest) interpretation, and even by RAW (Rules As Written) members of Always Chaotic Evil races can redeem themselves if they choose, they just really rarely do so. And card-carrying part is not required too. A lot of sourcebooks and even more literature works recognise He Who Fights Monsters, Well-Intentioned Extremist and Knight Templar as types of Evil too. In fact, sourcebooks go out of their way to point out that lesser evil is still evil and you don't do yourself and your alignment any favors when you go down that path. However, if you do want a Card-Carrying Villain character, the system does indeed encourage you.
And now 4th Edition has tossed out the second dimension of alignment. The law-chaos scale determining another portion of one's mindset is gone, so now alignment is simply determining just how good or evil you are.
Debatable, since alignment in 4th Edition has absolutely zero effect on your character (no penalties for acting out of alignment, no "Evil" or "Good" spell descriptors, etc.), it could be said that alignment is now only cosmetic.
5th Edition subverts this. There is no spell to determine what someone's alignment is (all Detect Evil or Good does is detect things deemed evil by the faith that grants the spell), and there's no particular penalty for acting contrary to your alignment, only any formal moral codes you might have. Evil people are generally implied to be very selfish rather than reveling in being evil in the Backgrounds as well. The Always Chaotic Evil races are also said to have memebers who buck the trend and are usually given explanations for their behavior (aboleths, for example, are all actually the same Lawful Evil creatures who oppressed the world in The Dark Times-they reform in the Plane of Water if killed).
Exalted gives us the Infernal Exalted; while they aren't Always Chaotic Evil, the cards are stacked against them. For one thing, if they go against the will of their Yozi masters, they accrue Torment, which can backlash and affect mortals in nasty ways. The only way to bleed off torment is to engage in Acts of Villainy — stick your foes in death traps, force an innocent into an arranged marriage, monologue at your archnemesis, etc. This is what happens when the guy behind the plan is the cosmic embodiment of douchebaggery. Mind you, it's doesn't say who you have to perform some of those Acts of Villainy on...
And then there's the whole reason they're like that — the Ebon Dragon had an active hand in their creation. Each of the Primordials represents a principle of Creation, and the Ebon Dragon once represented betrayal. Every thing he does is based around screwing someone over, even if it screws him as well.
The Devil-Tiger Dharma of Kindred of the East combines card-carrying villainy with punch-clock villainy. The path to enlightenment the Devil-Tigers walk expects them to be magnificent devils, both in the wickedness they perform and the punishments they deliver to sinners - even devils have their place in existence, after all, and that place is the punishment of evil. The Devil-Tigers throw themselves into the role wholeheartedly, devoting themselves to its pursuit.
Volrath from Magic: The Gathering was just absurdly over-the-top in how eeeeeevil he was. "I once had a race killed just to listen to the rattling of their dried bones as I waded through them." To be fair, he was R&D's first real attempt at creating a Big Bad, and, as it turned out, he was The Dragon to someone just as evil but with no bloody time or inclination for theatrics.
They subsequently created a new variant for casual play called Archenemy, a one-vs.-many game where, by dint of being the Big Bad of the game, the outnumbered player gets a number of benefits, including use of a "scheme" deck, a set of cards (that actually have the type Scheme) maintained separately from the library that give special benefits (usually for free) once per turn. (The idea is that the Archenemy is such a threat that other Planeswalkers have put aside differences and banded together to stop him.) The kicker is that each Scheme has a grandiose title (usually accompanying an equally devastating effect), often degenerating into card-carrying villainy, and some darkly appropriate flavor text. For example, Behold The Power Of Destruction destroys all nonland permanents target player controls. The flavor text?
I'd call that a successful first test. Golem! Rearm the Doom Citadel!
Certain Imperators (and possibly their associated Powers) in Nobilis will be like this, with Devils and Magisters of the Dark being the most obviously villain looking and acting (although Third Edition made this a bit more complicated; Devils are motivated by compassion for all things, especially ugly and corrupt things that have nobody else to love them, and are affected by that depth of affection, and Magisters of the Dark champion absolute freedom, especially the freedom to act against your best interests and destroy yourself). Of all Imperators though, the clearest example is Lord Entropy, the Darkest Lord, who wants to be feared by everybody and hates love to the extent that he made a law against it just to have something he could punish everybody for.
Chaos and the Dark Eldar in Warhammer 40,000 take delight in being on the extreme wrong side of the Moral Event Horizon. Considering the latter group lives off of Squick taken to the point of nightmarish, this is perhaps understandable. A quote from the nearest thing they have to a leader: "Death is my meat, terror my wine."