According to this here site, the knot I've been using for a very long time is the Uniknot, which I actually got out of some non-fly fishing book after getting fed up with clinch knots.
I used the Clinch knot and Improved Clinch knot for years because that's just what everybody seemed to use. They are both horrible knots. I don't mind losing a fish on a tippet snap, but there's nothing more frustrating than losing a fish and having that little "your knot slipped or broke" tail at the end of the line.
The Uniknot can be just as fast to tie as the clinch knot, and unlike the clinch, it cannot slip. I believe it to be stronger as well since it doesn't rely on compression to hold tight. Two of these knots together can also replace a blood knot (since the blood is simply two clinch knots), but you have to be slow when cinching it up.
I think that the six turns recommended in the diagram are a bit much though. For a small knot I use only three. For a bigger knot I use four. Never any more than that. (I'm one of those guys that's paranoid about tippet and knot size)