Actually I dont quite agree with what Goldorak said. The dilution cannot determine the contrast, because there are many other things that also have effect on it (temperature, agitation, developing time).
Rodinal is a high acuntance developer especially when diluted. The more you dilute, the longer the developing time will be normally. If you dont agitate much more, you will get more acuntance ("edge sharpness") when you dilute Rodinal. The grain will also stand out better.
Also if you dilute a developer and agitate relatively rarely, you will get a compensating effect for the tones as was probably said before. Highlights will not blow out so easily, so the shadow detail will (at least relatively) be better.
Rodinal is also often said to be one of the rare developers, where 1+25 or stronger developer will actually make the grain look kind of big too. The grain will be blurred but not smaller. This is mostly hear-say, but I kind of think I noticed this kind of action when I was a beginner and developed a Delta 3200 in 1+25 solution.
Almost everywhere that I read, 1+50 or milder dilution is recommended for Rodinal. For some films (APX?), the times get quite long thoug...
I use Rodinal for most or all films slower than 400 ASA and sometimes for faster films too. Usually for fast films I use Xtol for better shadow detail and film speed and more compensating development and a bit more "sophisticated" grain (I wouldn't say "fine" and I'm not allergic to grain and I also dilute Xtol so it wont blur the grain too much).