I never figured out the multiple ending system in Silent Hill 2. I thought I had, but the second time I played it I got a totally different ending (which felt completely unwarranted by the way), and then I hadn't done much different between both playthroughs.
There're a six endings. The first three are the "organic" regular endings and you get one of them based on your overall behavior around certain characters and items that is INCREDIBLY vague and hard to gauge. The other three you can only get if you follow very specific instructions during a replay, and at least 2 of them are joke endings (which include the dog one).
I did a mini cue card guide for this but like I said, the regular endings are hard to predict.
It's the only Silent Hill game to do multiple endings "right". Every other game has you either trigger a specific event or choose X over Y during a Plot Twist, adding up to a predictable result.
In the first game it's all about whether you save Cybil and do an incredibly unintuitive sequence of events known as the "Kaufmann sidequest".
In the third and fifth (Origins) games you get the canon ending first time, and a bad/joke ending on a replay if you perform X. Silent Hill 3 is easy to gauge, you have to score X points by killing X enemies.
In the fourth game it's based on whether a certain character dies during the final boss fight, and just how fucked up your apartment is at this point. That's two variables, so you get one out of four endings.
Homecoming and Downpour do the Crucial Choice thing several times.
Shattered Memories is the one that comes the closest to an organic multiple ending system. While you can force the ending through a set of Crucial Choices, these are completely masked (and feel quite random). I think the questionnaire you fill in at the beginning also makes some sort of impact. Actually the system is super weird. There're three kinds of endings, and then after one of these plays, you get one out of four possible "epilogues". I think Round 1 of endings was easier to predict than Round 2. Then again Round 2 doesn't have much narrative impact on the story, basically a home video plays to let you know what kind of life the protagonist led up to that point.