I just mailed out my tax returns (federal and state) today,¹ so they won't make it into the government systems for a little while yet. Still, for my own future reference (and for those of you who are prompter than I am), here's a reminder from last year: The IRS has a "Where's My Refund?" site which can give you an estimate as to when you can expect to receive your money – assuming, that is, that you overpaid the government and have money coming back.² Your state may or may not have a similar service available.
¹Which beats last year, when I sent them out on April 14th.
²I do, from both the federal government and the state of Maryland.