They really don't, though. The Sacred Cows thread has a couple of people say they don't like alignments, and has one post (by Agita) listing games that do not use alignments (which does not answer Necro's question). The "How do YOU interpret Alignments" thread does not talk about other systems at all, and is instead about how people interpret alignments in D&D.
Now, for Necroscoop: most games do not use alignments, and the ones that do usually don't look much like an alignment system at all. One alternative that I see pretty often is a "corruption points" system: for example, the Dark Side in Star Wars Saga and Corruption and Insanity in Warhammer 40k RPGs. This is more like Taint from Heroes of Horror than alignment, but Heroes of Horror does say you can use taint as an alternative to an alignment system.
The idea is simple: instead of being categorized by your personality, corruption points track evil things you have done and evil things you have been exposed to. No judgment is made as to intents or morality, as that is not the point: a person can fall to the Dark Side or twisted by the Warp without being a bad person up to that point. However, his experiences have consequences and different mechanics reflect and interact how far down the Dark Side you are. Evil, in this case, is like a disease instead of a personality type. Those who are touched by the Warp need to be destroyed, even if they are innocent, because they are a danger to those around them whether they want to be so or not.
Another way is to track reputation, kind of like Honour in Unearthed Arcana. Instead of looking at what a person things or what they have experienced, the mechanics track how a person is perceived by society. I think Legend of the Five Rings has a similar system, though I am not certain as I have not played it. Evil, in this case, is a social construct, though it still has a real mechanical effect because people react differently if you are famous rather than infamous.
In short: Alignment is about a person's motivations, Corruption and Insanity is about a person's experiences, and Honour is about a person's reputation. Any one of those can be used, together or individually. Or you can use none, like most systems do, since a person can be a bad guy without the rules telling you so.