What are some alternatives to wall anchors?
An alternative to using a large wall anchor for heavy duty mounting is to always find a wall stud for whatever item you are hanging on the wall.  Then you can use a smaller gauge screw (or nail) without any type of anchor required.  This will leave a smaller hole in the drywall and give you all the strength you need, but limit you to the places where you can position the item.

I am not sure what the weight of the item is that you are looking to hang on the wall but another alternative could be to just use drywall screws without any wall anchor.  In my house I do this a lot with light pictures, etc.  A drywall screw positioned at a slight downward angle has a good amount of holding power especially if it is something that is not going to get a lot of use but just sit there (I do not recommend just a drywall screw for something like a coat hook).

And then you can always use picture hangers like this that would only make a small nail hole:


Or even those sticky Picture Hanging Strips like this: