I don't know how bad for the eyes it is, but one thing you should do to limit the damage is to make sure the displays aren't too bright. My optician told me they should be as dim as is comfortable and don't sit too close. Also try and set the background to darker colours if possible. Most programs and web-browsters etc... have white backgrounds, which isn't good for the eyes.
This is something I don't have to deal with..yet... Our eldest is 7yrs old and whilst he does play computer games, he mixes it well with playing with toys, reading, jigsaws, lego etc... so doesn't spend too much time in front of screens. But in a couple of years time....who knows. He wont be having a mobile phone for many years yet though. A friend of ours has just let her 10yr old son open a Facebook account, and I have to say we're shocked that she's allowed him to. Ours wont be on Facebook at 10!
