I was specifically thinking about the Crisco shortening that is used in baking.
You can use any neutral flavored oil, such as vegetable or canola oil. You can also use butter, but you may have to adjust for the amount of water present in the butter (about 20%), unless you're using clarified butter which is a 1:1 substitution.
Lard. ... and to build on what @bmargulies said:
Other coconut oil, lard is one of the few fats that are solid at room temperature, and the only reason for using shortening in baking that I'm aware of is to get the little lumps of shortening mixed with the flour that don't melt until it's baked, which will result in a tender texture.
You can achieve the same thing with butter, but butter also has water in it, so you'll end up with some extra lift in the pastry, which isn't always desired for recipes that call for shortening. It also melts at a lower temp, so you have to start with it cold and work quickly.
... now, the other use of shortening in baking is for greasing pans -- again, it's because it's solid, so it'll stick to the sides of the pan. For that, you can often use canned cooking sprays, as they have surficants which will keep them from dripping.
An excellent substitute is coconut oil, because it is solid at room temperature. If you use vegetable oil, it will give the resulting baked good a much more oily texture.
I bet this isn't the answer you are looking for, but there's always lard.
Whole Foods sells an alternative to Crisco that I've used successfully. I don't have a tub here right now to get the brand.
I recommend clarified butter, especially if you clarify it yourself, or brown butter, especially if you brown it yourself. It takes a few minutes, and you need to let it cool down again before it becomes solid, which can take a few hours, but it lasts much longer than butter once you do these steps.
I've found it a much more flavorful alternative to shortening, and it offers most of the textural advantages.
I usually use applesauce instead of oil for banana bread. I was out one day so I used yogurt instead. It works great. I did an even exchange. One note, if you use Greek yogurt, decrease the amount because it will overpower the rest of your flavors.
There is an organic shortening just so you know...
I recommend coconut oil for the same reasons already posted. Then there is butter. Both of them have the same amount of calories. The same with organic olive oil.
I do not recommend canola oil if you are wanting to be organic. It is made from the rapeseed and the rapeseed is a genetically modified product.
Clarified butter will not spoil if it sits out just like shortening. But olive oil can go "smelly" after a couple of days which will affect the taste of your baked goods.
Rendered bacon fat after it hardens. It's a tasty substitute.
Shortening gives baked goods the soft effect that butter would not. Some cookie recipes call for both to get the flakiness of a good cookie and the softening for the softening so it won't be to crispy. Lard will give you a stale flavor as it is a meat by product. And coconut oil does not have the same effect as shortening that I am aware of. We need a chemist, ALTON BROWN WHERE ARE YOU!!!!!! Lol.
I always use applesauce in place of shortening in banana bread. Applesauce does not change the texture or flavor. I substitute it for equal measures of shortening.