Yes, InboxDollars is a legitimate rewards program that has paid out more than $60 million since it was launched in 2000. You won't become rich by doing things like collecting InboxDollars, since most tasks will pay you less than a dollar.
It's worth checking out if you want to earn some cash doing the tasks that you choose to do or the surveys that you qualify for. However, InboxDollars estimates that most activities will pay between $0.02 and $5.00 per hour.
Your money will be credited to your account right away after you complete tasks. It generally takes 3-5 business days for a company to process a payout request.