http://www.bigcommerce.com/

...this place impresses me.  It's a huge site, and as I scroll down every page, I find myself saying, "oh, that's a nice feature", or "I don't need that feature right now, but I will in a month or two", etc.

Features:
http://www.bigcommerce.com/features/

Apps
http://www.bigcommerce.com/apps/

...apparently they set your store up on a subdomain and pass you juice, as well.  I'm trying to figure out if you use your domain, if their is any love passed on as well, or whether it's better just to use their subdomain.

It was even better when they offered it self hosted (http://www.interspire.com/). That was good! but they axed it in favour of the hosted version, boo them
I must admit though, they do push it, a lot. They try and get as many places to integrate with it which makes it's a good Magento alternative IMO

But if you use your own domain I wouldn't of though you got any benefit as you can't 301 it, you can only use a CNAME or change the NS.
Well that's how I understand it, my knowledge could be completely inferior here

I have a couple of big commerce carts and they're OK, although they are slow to make changes as suggested by customers in their support forum. 

Bigcommerce is one of the most feature rich hosted shopping cart. It offers 24/7/365 official support and high level of security. It would be a nice solution to an online business briskly and without efforts.

" briskly and without efforts"

Oh. That's good then.