When my husband and I were vegetarians his favorite dessert was cheesecake. I actually did not like it that much, so when we became vegan it was no big loss to me. Several months ago, however, it was his birthday and I thought I'd try to make a vegan version. I am a big one for following recipes pretty closely, so in the end we did not like it that much, but it set my husband on a crusade to perfect the recipe. We have since discovered, through the trial and error of multiple cheesecakes, that it is best made with chocolate. Chocolate does solve a lot of things in my mind, and it has surpassed the task with this recipe, which my husband made.

Vegan Chocolate Cheesecake
Based heavily on Fatfree Vegan Kitchen's Vegan Eggnog Cheesecake [1] -- When I originally made her recipe, I didn't eliminate the "eggnog" associated ingredients (aside from the vegan eggnog), which is probably why we didn't like it as neither one of us are fans of eggnog.
Preheat the oven to 350 F. Drain the tofu and put it and the Tofutti cream cheese into your food processor. Blend until smooth. Add the sugar and milk, and process again until sugar is dissolved, about 3 minutes. Add the remaining ingredients (except chocolate and crust) and process until completely smooth, about 3 more minutes.
Melt the chocolate in a microwave safe container to a point that it is soft enough to blend with the other ingredients. You can also melt it on the stove in a double boiler.
At this point you need to decide if you want a cheesecake that is completely chocolate or half chocolate and half plain cheesecake. If you choose to do the first add the chocolate to your blended ingredients and blend again until the chocolate has been fully incorporated into the mixture. If you choose to do the latter, then pour half of the blended mixture into a separate container (or straight into your pie crust if you want plain on the bottom and chocolate on top), and then blend the chocolate with the remaining half that is still in the blender.
Pour the blended mixture(s) into the pie crust and bake in the middle of the oven for about 55 minutes (do not allow to brown). Filling will be slightly jiggly, not completely set until chilled.
Remove from oven and allow to cool. Refrigerate until completely chilled (the longer, the better).

We only allowed this to chill for probably 2-4 hours before we had a piece. The texture was still soft, and it was smooth. The flavor was rich - I imagine it was enhanced by the hazelnut milk that we used, and if you have ever tried Nutella you'll recall that it is a chocolate-like spread made with hazelnuts.
After letting the remainder chill overnight we had a much denser cake:

I think that there are two key things to making a vegan cheesecake. First, it has to have the right consistency. Cheesecake has a very thick and smooth texture, and part of the whole experience of eating cheesecake is how it feels when you take a bite. It has to feel creamy, thick, and fattening. It has to feel like an indulgence.
Secondly, the taste has to be there. True, I doubt that there will ever be a vegan cheesecake that tastes exactly like dairy-filled cheesecake, but at the same time ingredients like chocolate can certainly make you forget that it is vegan. That is the nice thing about this recipe - you honestly cannot taste the tofu and Tofutti. It doesn't have to seem fake - and well, honestly, it isn't. Who said that vegan cheesecake is fake cheesecake? It still tastes and feels like an indulgence.

Links:
[1] http://blog.fatfreevegan.com/2006/12/vegan-eggnog-cheesecake.html