Any vegan plain yogurt will work, as long as you don't overheat the soup after adding. Other options include the vegan sour cream options. You could also reduce some soy or rice milk, cool, and add vinegar to give it some tang. I'm lactose intolerant, so I've had to deal with this issue a lot.

I agree with hillarybee that coconut milk is the way to go. I use the light, unsweetened kind. Add it slowly when the soup is warm so it doesn't break. It adds a fruity richness to soups, sweet potato puree, even macaroni and cheese. Here's a great recipe for Butternut Squash Soup: http://www.danaslatkin.com/kitchen/butternut-squash-soup. Have a yummy Thanksgiving!

Try using a panade with a little bit of white vinegar. The panade will thicken the soup and the white vinegar with add the tony bit of acidity that sour cream adds to soups. After the soup has simmered for the given time blend it with a stick blender or a regular blender to achieve a creamy consistency. I have made my cream of tomato soup this way for year.

sorry, "little"

sometimes a potato can make a pureed soup a litelt silkier and creamier. with fennel/carrot a yukon gold would work (1 diced in with the carrot) and with the squash,perhaps half a sweet potato?

I agree that this is a finishing element. If blended really well, it shouldn't matter if you add dairy or not. I usually add coconut milk to my butternut squash soup to give it some added creaminess. It also adds a nice warmth and complexity of flavor that sour cream would not.

Make a veloute with roux made from vegetable oil. Dairy in this type of soup is for finishing so add your sour cream in the end. Remember cream or dairy in this case is for finishing not for thickening so most of these answers are a little off base.

Oh! Also, when I make butternut squash soup, I blend roasted pecans or hazelnuts into it with a blender. It makes it thick and creamy, adds protein, and keeps it dairy-free. Walnuts or almonds have the same effect, but the flavor isn't quite as nice in my opinion.

I wonder if you could thicken with bread crumbs, like a gazpacho?

Most of the time, a very good blender, like a Vita Mix will do the trick and you do not need to any any sort of cream or thickener. Should work like a charm with the squash soup.

Coconut cream or coconut milk can be a great substitution. I also use vanilla soy yogurt sometimes, depending on the recipe. For those soups, I'd try coconut cream first. Add less coconut cream than it calls for sour cream and taste as you go. You might end up wanting to add cider vinegar to balance out the sweetness of coconut.

Vegan Gourmet make a non-dairy sour cream that is really good. Same with their cream cheese.