This page contains some sequences, mostly from the endgame, that I use somewhat often. Some are very common, others I've only ever used once or twice. Corrections are welcome, as I'm sure I'll make mistakes.
Imagist (10 stones later) This page is somewhat embarassing.
First Line Standard Reduction
These first few plays are variations on the first line standard reduction. The standard reduction has the dual benefit of reducing white's territory by 2 while keeping sente (unless Mutual Damage is played).
( at ) Note that white must respond with from the previous diagram, or the marked stone will have done nothing to block black's invasion.
Herman Hiddema: This sequence doesn't work. Black can push trough at a and capture even more white stones. Also, black could play at . Try looking at what happens if white plays at ...
Imagist: I'm pretty sure this works.
Herman Hiddema: Note that in the previous diagram is at , so in this diagram is not required (or even possible) as there is already a black stone there. Which means black can cut with (at ).
This assumes that white has sufficient control in the area to kill and . This is useful if white wants more influence to the left (i.e. for protecting a corner from a 3-3 invasion) or if there is already a white stone at (so white knows not to waste sente).
KGS 5k: Consider this followup, , , , or , and the whole thing running along the second line... While I agree that if the marked White Stone was in place before you may take sente (given you have not to fear Black living inside or being able to reduce you), it doesn't impress me as a sort of influence to the outside. Instead Black may use the bad aji of the white group running on the 2nd line to invade with better result. Don't he?
KGS 5k: I most likely would play like that. "Taking sente" but with less bad aji and giving away two points. Most probably Black will not play out the 3 to 5 gote sequence, though. But in reference to a feared invasion on the left side it looks better to me than your version above.
After seeing that variations 1-3 work, a beginner might think that will work also. This is a terrible mistake. (Note that given the situation, white should play like in the above diagram marked "White Must Respond". The line of play shown is only to demonstrate that running along the wall to doesn't work).
Second Line Standard Reduction
These plays are variations on the first line standard reduction. This reduction reduces white's territory more than the first line reduction, but it also has the risk that black will end the sequence in gote, since it is often to white's benefit to play tenuki instead of . It also leaves some aji for black at a.
Even worse for white, in some situations white will have to play , to prevent black cutting at a or b, so the situation ends in sente for black.
Black must respond to white's response, as is the second line reduction on black, and black's initial reduction becomes purposeless.
AJP: This is not quite true. Black can use as a sacrifice in order to block at in sente. This is quite useful if the life/death status of the black stones is not yet firmly established as a simple descent to is not necessarily sente against white.
Bill: I think rather that under certain circumstances Black may play in sente to prevent White from playing the descent at . He might also play it as a losing ko threat. Otherwise, Black is typically worse off after the exchange, - . That's why Black normally continues at or a. See reversal.
If white does not respond, to is tewari for a first-line invasion to which white did not respond. However, the second-line invasion is often played early enough in the game that this is not the biggest placement on the board, so it is often to white's advantage to play tenuki.