I got lucky - DH & I hired a woman based on a referral from our real estate agent when we bought the house. Turns out this cleaning lady is the agent's cousin. We ended up not trusting our agent at ALL, but the cleaning lady has been wonderful so I feel lucky. She's licensed and bonded and owns the business herself. She had a crew of 2-3 girls she used to bring with her but after the economy tanked she scaled down so now it's just her and her husband. It takes them a little longer but the price is the same and the work is just as good so I don't care.
We have an electric combo lock on our front door so we just gave them the code to the door. DH works out of the house so sometimes he's home, sometimes not, sometimes for part of the time. They come and go as they need to.
At first we were nervous about it but they've been great so we don't worry anymore. A couple minor things have been broken but they never hide anything and have always offered to replace or pay for things so we don't worry about it - mistakes happen. Nothing has ever gone missing, except for a vacuum attachment that I think must have gotten thrown away somehow, as they don't have it and we can't find it!
We actually tried another (cheaper) cleaning lady for awhile but it was really bad. Another lady who owned her own business, but she was very very short and wouldn't use a stepladder or a long brush, so the upper parts of the shower started to mildew, upper cabinets never got wiped down, etc. Plus she'd leave grunge behind on the kitchen counter and when we asked her about it her answer was, "I don't scrub. I wipe, but not scrub." Um...but that's what we hired her to do! We went back to the original people (who don't mind scrubbing when necessary) and we don't try new people anymore, LOL.