Will Chrome extensions have access to all my private data and browsing history

When I install, Chrome warns me that AdBlock will have access to all my private data and browsing history!

It's true. AdBlock has the ability to access to your private data, but it doesn't actually access it. In order to remove ads from every web page, AdBlock needs the permission to run on every web page; and any extension that runs on every web page has the ability to see everything you're doing and what URLs you visit in which tabs.
Specifically, you're warned that AdBlock has access to "Your data on all websites" and "Your tabs and browsing activity" - but these are only used to block ads for you.
In Firefox, the situation was worse: every extension had the power to access your private data, and you weren't informed. In Chrome, at least, those extensions that need to run on every page show you a warning before you install them!
It comes down to trust: you should not install extensions that ask for more permission than you are comfortable with, unless you trust the author(s). AdBlock is the most popular extension for Chrome, partially because we care so much about our users -- so we hope you'll trust us :)