The answer is.....
The answer is of course.........'it all depends'!
3-5x depth, given a good length and weight of chain should do the trick in most condidtions. Obviously, the chain element of the rode is probably responsible for 50% of the anchor effectiveness. I tend to carry 20m if 'lighter' chain if going offshore, to keep weight in the boat down without sacrificing too much anchoring power.
Will also sometimes carry 2 anchors. General allrounder like bruce or danforth and a grapnel for any rocky bottoms or as a spare.
The safety element of anchoring is not to be under estimated of course. I will always encourage students to consider anchoring as a primary means of keeping themselves out of trouble in the event of engine failure, particularly in large busy harbours. As such, I would recomend keeping you anchor and rode to hand at all times in a bucket or similar, as near to helming position a s possible. If your bow line, attached to your D ring on the stem, is also lead back to the helm area, then you should be able to connect and deploy the anchor in a matter of seconds. Carbines or caribiners can also be used for a quick method of attachment, but shouldn't be relied on long term.