I'm not sure it'd be possible to make a good competitor to Now without tracking what someone does all around the web. That's sort of the point of it - the more it knows the better it works.
The most useful things I get from Now are travel info (mostly comes from email/calendar), sports scores (I have to set these up manually), flights details (again from email), deliveries (again email). So they can do quite a lot with just email and calendar access. If you use iCloud they already have these things and don't sell ads against them so you can get some of the functionality (imo the best parts) without tracking. What parts of Now do you think they couldn't do without heavy tracking?
They clearly couldn't do "new posts from sites you read" and "people who read the sites you read liked this article", which are very nice Now features. I suspect they'd struggle to do "recommended restaurants/museums/etc. near your current location" - Now seems to have figured out my restaurant price range (for example), and I can only assume that was through tracking.
