In reply to GarethSL:
I think what to clip and how many ropes to clip with is totally situational. Some of the conditions affecting the decision:
1. The difficulty of the beginning of the pitch. At some point, climbers have to put their faith in climbing skills rather than protection systems. If the climbing is easy for the leader in question, it is reasonable, , and in my experience utterly commonplace, to climb up 5--10 feet or so to a first good piece without clipping anything to the belay anchor.
2. The anchor type. If you have two modern bolts, it will usually make sense for the leader to clip one of them (but see Item 3 below). If the anchor is a gear anchor and clipping it seems prudent, then I think one ought to set up a power point if possible and clip that, i.e. distribute the fall load to the entire anchor and not just one piece. (But again, see Item 3 below.) If we ignore the belayer skill and ability and focus only on the anchor load, then the leader only has to climb a few feet before it is better to catch a factor-2 fall rather than, say, a short factor 1.7 fall through the anchor, as the factor 1.7 fall will create a much higher anchor load because of the pulley effect. This higher load isn't a concern with modern bolts, but might be with gear.
3. The anchor position. A lot of anchors aren't high enough to avoid belayer-anchor carabiner collisions if the leader falls. If such a collision happens, either with the belayer's non-brake hand or the belay device, the robustness of the belay is unpredictable. So either the anchor ought to be suitably high (not that many are) or the belayer has to be held down with a directional (which isn't always possible).
3a. If there is really serious climbing for the leader directly above the anchor and no possibility of obtaining an independent protection piece, then the best (though inconvenient) strategy is to situate the belayer well below the anchor (quite possibly in a hanging position) in order to reduce the fall factor associated with a fall directly onto the anchor.
As for rope clipping, there seems to me to be very little reason to ever clip both half ropes to the same piece, but the anchor is one time one might do this if the party anticipates a reasonable runout above the anchor, because the belayer will have better control gripping two ropes rather than just one.