I put "privacy" in quotes, because under the scheme below you're still giving up a lot of data, but you can (I think) still maintain "silos" of data so that, for example, your search data isn't correlated with your YouTube or GMail data.

See What Actually Changed in Google’s Privacy Policy from the EFF for a good description of the substantive changes in Google's new privacy policy.

Here's what I'm doing to try to preserve some of my data in silos. This is based on my understanding of the way the new privacy policy works, which could be faulty. Remember that you're still giving up your data by using these services.

1. In Firefox, I've installed Duck Duck Go as a search engine, and I use it as the default. I've been using this for months now, and it doesn't suck. The results are almost on par with the results I used to get through Google, and they have a surprisingly "private" privacy policy.
2. In Firefox, I've installed Ghostery. This blocks all kinds of trackers, including Google Analytics.
3. I've switched from using the GMail web UI to a desktop client. Google still sees all my email, but I don't have to remain logged in to that account in the browser. (See #4.) This effectively makes the mail account a silo; none of the data is used elsewhere. I occasionally have the fantasy that I'm going to move my domain off Google Apps and go back to self-hosting, but that's unlikely to happen in the near future.
4. When I'm browsing, I'm logged into a second Google account that is disconnected from my primary mail account. (See #3.) This means that, for example, videos that I watch on YouTube aren't correlated to the content of my mail.
5. In Firefox, I've installed Adblock Plus. This cuts down on tons of ads; which might avoid leaking your data to advertisers.
6. I haven't done it yet, but I plan to find a desktop RSS reader that doesn't suck and delete everything from Google Reader.
7. I've stopped checking in at Google News. Instead I pick one of CNN, News360, BBC, or other news outlet.
8. I'm not sure what it would be, but if I'm browsing stuff that I don't want tracked, I'll fire up a Chrome Incognito session and proxy everything through Tor. (The only reason for using Chrome is that I typically don't want to interrupt a Firefox session to drop into Private Browsing mode there.)

It's worth noting that I don't use G+, so I'm not doing anything specific to maintain a silo there.

As noted above, most of this doesn't vastly enhance your privacy. You're still handing out a lot of data every time you browse the web; it's a fact of life. And it is, after all, very convenient to have access to your search history -- I often find myself trying to figure out what that thing was that I found during a search a couple of weeks ago but can't remember the terms I used. But I'm hoping that it cuts down on the amount of data correlation between my various online activities.