Up until this point I have been relatively naive when it comes to the various cuts of beef and what their best uses are. With a slow cooker the general rule of them is that the slow cooking will tenderize even the toughest cuts of meat. However, my inclination would be that the better cut of meat you start out with, the better your results could potentially be. I think the main thing is you want to make sure you are using meat with a decent amount of fat in it which will allow it to become moist and tender during the cooking process.
The breakdown of the different cuts of meat and what they are used for can be found on Wikipedia and is a handy reference guide for what cuts of meat are best for what types of purposes. When I look back on what I have made so far I have found that my best results have come when I have used brisket and plate steaks (such as hanger or skirt). A lot of this has to do with the amount of fat that these cuts have, which compensates for them not being very tender and lends them so handily to slow cooking. Long story short, make sure that your meat has some fat on it to ensure you get a nice moist, tender result. Same holds true for pork where the pork butt (of the shoulder) has a pretty good amount of fat on it which helps baste and flavor the meat throughout the cooking process. Just talking about this is making me hungry!