I've got several recipes that call for shredded chicken, so any help would be appreciated.
I keep both shredded/chopped chicken and pork in my freezer as kind of a "staple". For both, I tend to use the crock pot.
The easiest way (but certainly not the cheapest) is to toss boneless, skinless chicken breasts into the crock pot with a flavorful liquid. I tend to use most of my shredded meats in things with either a Southwest/TexMex or BBQ bent to them, so I often will use beer for the liquid and toss in some chili powder/onion powder/garlic powder or one of those taco seasoning packets.
If you're looking for more wide-ranging purposes, you may want to go with something more like chicken broth as your liquid. In that case, I'd also avoid seasoning it all that much as the destination dish might clash with or, for instance, if you add salt, might result in WAY too much salt in the final dish.
I usually fill the crock pot all the way with chicken and about half way with liquid.
Set the crock pot on low and let it cook all day until the meat is completely cooked and tender. I only make it this way when I can be around all day or at least can check in half way through the day because you want to "rotate" which meat is sitting in the liquid at least once in the process.
To shred, pull out the chicken and, using 2 forks, pull apart the fibers of the meat.
To chop, just toss it on a cutting board and cut into tiny bits.
I usually take the results and put them in a large bowl. Then, using a turkey baster, I add some of the liquid from the crock pot back into the shredded meat. You'll be surprised how much liquid it absorbs without getting "drippy".
I freeze mine in 1 pound portions in vacuum sealed bags and it works great.
Faster than the Crockpot, you can poach chicken breasts in water, broth, or some other flavored liquid. Shred or chop once they're cooked (about 20 mins if memory serves). This leaves the chicken a little bland though. It's ok if it goes in a flavorful sauce which it so often does but not on top of a salad. If you want to use thighs, you can cut it in to thin strips first and then sauté. This gets the same effect as shredded and is how I do chicken for enchiladas.
However, the Crockpot sounds like a great option if you have all day to tend it.
When I cook chicken breast, my main concern is overcooking. "Stringy" chicken often ends up quite overcooked, with a "dry" texture even if it served in sauce. In my experience, crock pot chicken is always overcooked; so unless you are really looking for that texture, I would avoid it.
Poaching (as in the answer by @yossarian) is a possible solution; but you still need to be careful to avoid overcooking! Make sure to remove the chicken from the pot once it reaches the desired internal temperature (I cook to 150°F) as measured with an instant-read thermometer. There are some other tricks for a good poach, like starting from cold and keeping the water under boiling.
However, if you have the equipment, sous vide is better. It is more reliable and more hands-off than poaching. The water bath makes it impossible to go over the desired temperature. Further, by sealing the chicken in a bag with aromatics, you avoid losing any flavor to the surrounding liquid. A great place to start for chicken breast is 2 hours at 150°F. Obviously this technique requires some equipment: namely a sous vide circulator and a vacuum sealer. But if you like juice chicken breast, this is almost certainly the most reliable method.
A wonderful recipe from Yotam Ottolengh's "Jerusalem" cookbook uses shredded chicken breast in a salad. It says to generously season the whole chicken breasts with salt and pepper, roast in a oven-safe pan on medium-high heat to get a good crust going, then finish in a preheated 180 °C (360 F) to 200 °C (400 F) oven for 15-20 minutes. Check the core temperature with an instant-read thermometer to make sure it's cooked properly. Let rest a few minutes, then shred by hand or with forks.