At the heart of the Undertaker's character, one so heavily wrapped up in death, there has always been a sort of immortality. More recently that immortality has been one of nostalgia. Looking at his current part-time appearances, the theme appears to be that as long as the Undertaker is out there wrestling, then at least some connection to our own experience of the sport as younger, less jaded fans exists (Sidebar: This is the role that HHH so desperately wants to fill, and yet because he keeps talking about it so much he never will.). Prior to this, the "American Badass" character was an homage to a fading American concept of masculinity, the immortality of the lone wolf, forging destiny on the strength of indomitable will and, well, strength. These are effective standards to bear, and they, combined with Undertaker's legendary in-ring work and physical presence, are what have given Taker his "face pop for life" card.
However, it's easy to forget that there was a time when Undertaker was perhaps the most dreaded villain in wrestling. This was a man who kidnapped a young woman to get back at his boss, who claimed he lit his younger brother on fire (a fire that, as WWE cannon goes, is up there with "Lost" in terms of the convoluted mystery it has created). Hell, he tried to embalm Steve Austin, and when that didn't work his cohort was going to just straight stab him with surgical scissors. Obviously, his initial fanbase growing up and his continued presence in wrestling have given him the sort of warm glow that all of our heroes have, but it's worth pointing out that unlike Steve Austin or The Rock, Undertaker was for a time, completely devoted to the sort of evil that made parents wonder if they should let their kids watch his work on television.
The Ministry of Darkness came about as a result of one of WWE's many "blurred reality" storylines; Vince McMahon claimed that Mark Calloway had gone insane, and that he had completely become the Undertaker character (another sidebar: This is always a dumb explanation for things in wrestling. What was he doing before?). This came on the heels of Undertaker's attempted crucifixion of Steve Austin, so it was at least a little believable that Undertaker had become something beyond the sort of bedsheet ghost villain that he had played up to that point. What followed was a series of events that in my opinion set the stage for CM Punk's "shoot" promo work; Undertaker essentially going into business for himself and threatening to invade and infect the entirety of the WWE, recruiting wrestlers to join him as he sought to depose Vince McMahon. Acts such as the Stephanie McMahon kidnapping (preceded by Taker burning her childhood teddy bear) and the attempted "Black Wedding" to Stephanie ensued, with Undertaker spiraling further and further into a unique kind of darkness to the WWE up to that point.
It still all linked back to the same kind of immortal character that Undertaker's face work has drawn from; the only difference in the standard carried by the character. In this case, as a heel, Undertaker didn't carry the standard for nostalgia, or for country; he carried it for death.
That's the kicker, and it's why Undertaker worked just as well as a "serious" Attitude Era heel as he did as a Golden Era heel, and why the PG Era would never have him. Death is the inescapable villain, ever-present, lurking and waiting to pounce unexpectedly. There is no clear plan, and there is no clear motivation other than its own growth and expansion. For it to truly be conveyed with the dread it deserves, it must be ugly, and brutal, and unpalatable. There is no "fan friendly" package for death, and to try and do so is to immediately render its potency as an agent of evil moot. If it is controlled, it isn't really connected to death in any meaningful way; out of control, death is the single most terrifying force on the mortal plane, which is why they even call it the mortal plane.
Undertaker embodied this as a heel. It's why kids recoiled when he dragged Austin into that morgue, or when Stephanie's limo screen rolled down to reveal that he was driving; you knew he was coming, you just couldn't do anything to stop him. He hung their hero (unfortunately literally) in the center of the ring, powerless against the Undertaker as the weakest man on the roster. As with most great heels, all of this was crystalized by the man's in-ring work. That same "WHAT CAN YOU DO TO PUT HIM DOWN" presence and the urgency it creates in his matches? Now imagine it as an agent of malice, unstoppable, without fatigue, dispassionate. It was horrifying, and it gave every match the sort of tension that true villains create; each fight mattered because of the foe that was to be overcome.
Consider that Undertaker, the man that children cheer for insanely now, was once such a dark, looming, evil threat that he united Steve Austin and Vince McMahon against him. He was too brutally anarchic for the WWE's ultimate rebel, and too malevolently ambitious for it's own evil emperor. Undertaker was a threat to every side of the war. Then again, what could possibly be a better foe to unite against than death itself? Everything was rendered the lesser evil standing next to what the Undertaker stood for, bringing together the most powerful forces in the WWE against him. The fact that, even united, they still sometimes failed is a testament to the force that the Undertaker conveyed as a villain.
After all, when it comes to wins and losses, Death remains undefeated.