My husband decided to get our daughter an Asus Eee Pc series when she was just turning 4. She used to play on several childrens sites, and draw pictures.The Linux learning and drawing programs are great in my opinion.
The answers to one of the first questions I asked may also be of use for you.
My husband is responsible for all the IT stuff in our household and I am sure that he will take the necessary precautions regarding safe internet access, (as I am sure many of the parents on this site are)
I feel we have acted sensibly because even though Daddy is a programmer, (we have several desktops, laptops around our home (not to mention "android phones") and spends considerable time on his computer when at home, our daughter does NOT have an infatuation or an addiction with the computer or for the games and activities that it can be used for.
Pencils, paints, Lego, Jenga, Puzzles Dolls and Books still thrill her, as does her bicycle and ball.
I have had the opportunity to compare her behavior with children who have been exposed to computers much later and the difference is remarkable. They always seem to want to be on the computer, and the more the parents try and ration the usage the more the kids seems to crave it. I have even witnessed, time spent on the computer being used as a "punishment" with "no you are not going on that computer"
I am not sure I can give an age for internet access without parental safeguard, in fact this depends a lot on each individual child, family and environment.
In our case I do know that the little pink laptop sits on her desk in her bedroom, and if we both happen to be working on something in our office and she wants to join us, she will place it under her arm and come and join us, sitting at the end of my desk. If she has homework, we use my computer to research the topic together, and basically this is like using an encyclopedia.
ADDITIONAL NOTE: Our daughter is currently 5 and a half years old.