For my .02:
The convenience of Gmail outweighs the privacy concerns for me. I'm not worried about a bot reading my email to targets ads me. I generally ignore them anyhow.
Most people realize that 'free' services are never truly free. Look at the data mining Facebook does. Google is doing basically the same thing only the have access to the more sensitive information. Gmail sees more concrete information business transactions, receipts etc. Facebook sees more of the personal stuff.
Speaking of Facebook. I once read a study that Facebook can tell who you have a crush on and who your dating or would like to date and even when a breakup is imminent based on how often you view someone's profile or if in a relationship how often you view profiles of the opposite sex.
Earlier this year Google rolled out Google Now on Android. I didn't think it effected me much until I opened search on my phone and it told me my package from Amazon will be here the next day. It was a little creepy but cool.
Google also does the same thing with Maps. If I Google an address when I pick up my phone later it tells me how long until I arrive at that destination I can tap for driving directions. It's not perfect it doesn't know when I'm just looking at an address to get an idea of the area or if I actually plan on traveling there.
It's a little creepy but this is a synergy of sorts. My phone knows what information I want before I specifically ask for it. That's not something you'll hear me complaining about.
So far I trust Google. It hasn't done anything inherently evil to me. I damn sure trust Google over Facebook; Who insisted on querying my GPS every time I opened the mobile app despite having location services off.