Hi TabletNovice!
Which ones would you recommend?
It's almost impossible to find games without some type of nag screen. Some are very annoying and in-your-face, though they seem to bother an adult more than a child.
As others pointed out, look for parental controls to prevent children from buying additional stuff. These ads are so integrated into some programs that a young child would probably not realize they were purchasing something. Some ads are shameless, like dangling candy in front of a child's face, and not giving it to them unless they paid me. Some educational apps may require a monthly subscription to get a higher level of information.
Even apps you pay for may tempt you to buy other components in order to use the program more fully.
Anyway, I've been downloading some games and programs for the children. I will not be with them for a couple of weeks so I've screened the programs the best I can for now. I will watch closely when we are together.
Read the user reviews, especially those three stars and below. Comments can give you an idea about the amount of ads, and help you determine how much you'll let your children/grandchildren stomach.
Here are some I installed for my five year old grand daughter.
The "Maker Games" eg. Cake Maker, Popcorn Maker
Picsart Kids
Dress up apps (virtual paper dolls)
Puca
Picasso
Dr Seuss books
Jumpstart
For my grandson, who is 9:
WaterBalloons
Cogs
Bike Race
Ski Safari
Miscellanous apps:
Be a Martian
Hubble Space Center
Math Pro
Clouds and Sheep
TrueSculpt (virtual clay modeling)
The links someone provided above show a good selection of games for children. You just have to sort through them. Look at the Videos before buying. The provide a good idea of the content (though not the nag screens and ads).