So could someone working at your bank directly. Of at your HR department at work. Most of the wait staff at the restaurant I ate at technically had access to my credit card and could steal money. While you are at work, someone could break into your house and steal your stuff too.
The point is, Mint and everything else is a matter of the evaluating the risk. Since you already understand the vulnerability (they have your accounts) and you know the risk (they could steal your money) what are the chances it happens?
1.) Mint will make lots more money if it doesn't happen, so it benefits Intuit to pay their employees well and put in safeguards to prevent theft. Mint.com is on your side even if a specific employee isn't.
2.) You have statements and such, so you can independently evaluate mint. I do not just trust mint with my stuff, I check info in Quicken and at the bank sites themselves. I don't do them all equally, but I will catch problems.
3.) Laws mean that if theft happens, you will have the opportunity to be made whole.
If you are worried about theft, don't trust other people or generally get a bad feeling, don't do it. If you check your accounts online with the same computer you log into Facebook with, them I would suggest it doesn't bother you. You might have legal or business reasons to be more adverse to risk then me.
However, just because somebody could steal your money, I personally don't consider it an acceptable risk compared to the reward.
I will also be one of the first people to be robbed, I am not unrealistic.