@sanrensho
Gosh, where to start. First, from a performance point of view, in life and other sports in general, the core is often used to transmit rotational loads from the hips to the shoulders. Throwing, punching, running, carrying the shopping etc., all have this, and it's quite an important contributor to performance. At the basic end of things, every time you take a step, you put a twisting load on your pelvis (think carrying a big christmas present in its box from the post office

). In the extreme, e.g. in boxing or throwing sports, it's a performance limiter (the hardest punch you can throw is not dependent on your max bench press, it's dependent on the speed/recruitment of the core). I'm sure you can find better pictures of this, but the women's heptathon is a good case in point, these girls have awesome ab development and their anti-twist function during running is obvious (as it is with their other events).
http://www.standard.co.uk/olympics/athl ... 21948.html" onclick="window.open(this.href);return false;
Even on a bike you're in a similar place. E.g. when out of the saddle, your hips are rotating your pelvis one way, your arms are rotating the opposite, your core is transmitting this load. (And this is the one area I've noticed a distinct improvement on on-bike performance, getting out of the saddle and giving it beans now feels much more effective, I can really muscle the bars and keep my shoulders/back stable). (Google Serape Effect for more on this aspect of performance)
From an injury prevention point of view, there is scientific evidence that twisting and bending the spine at the same time is particularly bad. Developing the ability to withstand such loads is thus an important part of injury prevention. Bear in mind though that the other way to look at this is through flexibility mobility work - if twisting/bending of the spine places you in a compromised position, reducing the need for the spine to twist/bend through hip and shoulder flexibility work is equally as important. Stuart McGill has written lots on this, he has an excellent book and a number of papers to his name, also some interviews on the web to give you a flavour.
What this means in practice is to emphasise exercises that replicate this loading.
Don't bench press, use press-ups instead. Not only is the straight press-up a great core exercise (keeping your body straight, and it also recruits some important shoulder stabilisers - the bench has also zero core involvement), you can load it up in extremely challenging ways, also with rotational loading. E.g. raised leg, narrow/staggered hands, single leg/arm, chains, med-ball under a hand, clapping, blast strap. Lots of fun here! If you're wedded to the idea of benching, then the one good bench variant is a dumbell press with alternating arms (i.e. you only work one arm at a time, the other stays straight and loaded). Similarly, if you're shoulder pressing, do it standing and with one arm working at a time. One arm dumbell snatches are also interesting if you're up to it technically. Some more ideas here:
http://www.t-nation.com/free_online_art ... ch_press_1" onclick="window.open(this.href);return false;
Bridges, both regular (one-leg ideal!) or side bridges.
Single leg variants of both squats and deadlifts are great (as above).
Chin/pull-ups are essential (though make sure you do them with good form, bar to the collarbone, to maximise training effect of shoulder stabilisers). But you can have fun with rows: inverted blast strap rows, also with one arm; renegade rows (essentially a loaded 3-point plank, very challenging!).
As before, suitcase carries, palloff presses (bands are good for this

), and turkish getups are all great (should be obvious why by now!). There are other variants on the palloff press theme too, see this links for some other ideas (e.g. med-balls etc.):
http://www.t-nation.com/free_online_art ... e_exercise" onclick="window.open(this.href);return false;
http://www.t-nation.com/free_online_art ... training_1" onclick="window.open(this.href);return false;
Don't forget flexibility. Usefully, most of the above also challenge your mobility too, but (if you're like me and most other cyclists I know well!) you might require additional hip and shoulder work. Band stretches for the shoulder are particularly good; hips need hamstring, hip flexor, internal and external rotation work.
http://nicktumminello.com/2010/01/rotar ... e-missing/" onclick="window.open(this.href);return false;
Hope this helps!
@Tapeworm
"And I concur re Turkish get ups, very... interesting when they get heavy!"
As I said, "curiously entertaining"

. I must admit, i didn't get Turkish getups until I'd got the technique down and did my first "heavy", then the penny dropped and my other half got an excited my coming back from the gym going, "wow, this is a great *#!$ing exercise!!!".