We are contemplating replacing the tile and carpet with concrete staining. Will the marks from the tile show when the concrete is stained? Are the floors easy to maintain?

I have actually painted the concrete floors. The first was a bedroom which I taped off "grout lines" and painted with concrete paint and then used 3 different craft paints and scrunched of plastic bags. I sealed it with 3 coats of water-based poly. The living room was first primed with tinted kilz-it primer(grey)and then I taped off the grout lines and painted with concrete paint. I did a faux finish with glaze and gold craft paint using the plastic bags. I sealed it with oil based poly but wish I would have used water-based since oil-based yellows. The 3rd is the garage floor which I primed and painted with epoxy paint and concrete stain. I am sealing it with water-based poly and then industrial floor sealer. Very easy to maintain... just damp mop!

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Regarding the staining, I don't think you would get a good result with just stain, the pores of the concrete have been filled with glue from old flooring.
I think it would come out very spotty.
There are a lot of products that can make a very durable and goodlooking floor, but most require professional installation.

Good luck Roger

You can use Krud-Kutter avaiable at Lowe's or Goo-Gone to remove the adhesive. You will need to use an acid stain to stain the floors unless you etch the concrete first.