Tenerife seems to get a bad rap here, so I'm using my first post on mumsnet to defend it. The yob culture areas of Tenerife have given the whole island a reputation it doesn't deserve. I haven't visited any of the other Canaries yet, but Tenerife has much to recommend it.
Disclosure: My parents retired to Tenerife and then decided to come back to the UK. We enjoyed the area they were living in, and most other parts of the island, so much that we brought their apartment off them when they moved back. It's based in Golf Del Sur which is a quite resort with golf, horse riding, and sailing to hand. It's away from the clubbing areas, and tends to be more for the old-timers and families with young children.
Tenerife as a whole has some fantastic places to see and visit. For the kids the south has many amusement / theme park type venues, and if you're willing to take the 45 minute drive to the other side of the island, Loro Parque is a world-class Zoo that I can't recommend highly enough for families. The volcano caldera is an amazing spectacle for adults, but won't necessarily hold a child's attention for long. The forests on the higher regions of the mountain are gorgeous with great walks / hikes and spectacular views across the island and the sea.
The best parts of Tenerife for me though are the "Spanish" towns and villages. Every one has a park for the children to play in, and every time we've been to one, the Spanish children play really well with our kids. Sunday evening in every town Plaza is a lovely experience. The Spanish love to get the whole family out and eat, chat, and play together. It really is all about family and something I think the Spanish have right and we have wrong! And if you get the chance to have a visit when the festivals are on you in for a real treat.