For me it tends to fail on very specific queries and then I use it's Google Bang to just have it redirect me to Google. But it's as good as Google for my typical queries.
I use Mail.app w/ GMail over IMAP and have no problems. I could switch to any other provider of course, but see no reason to do so as accessing GMail over IMAP doesn't have any of this social crap associated with it. Unfortunately, on Windows I'm forced to use gmail.com as no desktop client comes even close to Mail.app's fully integrated and optimized IMAP support. Outlook's IMAP support is STILL blocking/synchronous for most operations, hanging the entire software while it syncs headers or sends items to be erased. Thunderbird is as clunky as ever.
Google is the only one left, then. I used DDG for a while, but I think they need to step up their game with regards to simplifying the UI (i.e. remove the attempts at finding the info you're looking for for you or at least provide an option to disable this) and speed up both page serves and queries, w/ geodistributed caching, etc.
Or you could just use Google SSL, but disable all cookies for that domain.
I had previously self hosted (a pain), and then used google apps with my own domain. That was when google apps had no google groups or other integration at all, and it was cumbersome to have two google accounts (no multiple login then either). So I switched to plain gmail. Certainly less work and the bonus of being able to tell people 'blah blah at gmail dot com' and not having to spell it out every time someone asked for it cannot be understated.
My needs have changed a bit though, and being able to retain my email/domain should I choose to change providers again has become more important. In addition, I no longer use the gmail web interface, opting instead to use sparrow over imap. An unlikely shift back to client centric computing even while more and more of my other services are shifting away!
Search, I still find myself using google from time to time, but my default search is duckduckgo, this is greatly helped due to the fact that it's simple to search from google instead by simply adding !g to the search, additionally, you can do similar things for !gmaps !gimages !bing, this feature alone makes ddg a trivially better google replacement for default search.
Now, a decent replacement for the gmail client, I haven't been able to find something satisfactory web-based, or even as a desktop app. I use thunderbird for work emails, but it seems to be a little... lacking.
Chat: IRC/AIM/Yahoo/etc - just grab something with a libpurple backend.
Search: DuckDuckGo most of the time, Google otherwise.