I've bought 2 bikes, so far, for my 2 kids. A Ridgeback MX-14 as a first bike for my oldest, and now still perfect for my youngest, and an Islabike Beinn 20S, which my oldest will soon outgrow. But once again the economics of buying decent bikes shines through, it will be perfect for my youngest, when he's big enough for it.
Both have been excellent and I'd personally go for another Islabike for my oldest, but he's taken with the idea of a BMX, so the next challenge will be finding a decent one for him.
Have to say I love the notion of decent bikes, that don't pander to whims or irrelevances, that are so well thought out and executed. They may not be the most enticing looking to kids, and the costs may seem steep, but either resale or reuse shows them to be pretty good value.