it adds flavor and moistness to the cakes thats why i do it.
CakesbyMark is right they had moistness to your cakes. I add a box of pudding in all of my cakes. I either use the flavor closest to what I am making or just use vanilla. I think it also makes them a little more dense so they are not a fragile as the typical box cake. I will never go back to not using pudding in my cakes.
I just recently became a pudding convert 
I wanted a denser cake but still from a box mix. I add an extra egg and one box of pudding to each box of mix. The cakes bake up higher and have a denser texture as described in other posts. Bonus, my kids and husband love it, and have asked me to never go back to plain cake mix 
I do the same thing to..
1 box of instant pudding
1 extra egg
up the oil to 1/2 cup
It's been a hit with my clients.
For extra moistness, Moxey2000 adds pudding mix to the mermaid bakery vanilla butter cake along with extra milk. It is a scratch cake. I've attached the link to the recipe - the addition of the pudding and milk is mentioned in the comments. I'm going to try it next time I need one for work. I love the WASC, but I am trying to get some good scratch recipes that hold up to stacking, etc.
http://cakecentral.com/recipes/4313/vanilla-butter-cake-from-the-mermaid-bakery
It's just for cake mixes. NEVER add to a scratch recipe.
I happen to have a recipe for a scratch pound cake that calls for a small box of vanilla pudding. It is the most moist, excellent pound cake I have ever had. It made me think twice about adding a box to other scratch recipes. I just have not tested it out, yet.
For extra moistness, Moxey2000 adds pudding mix to the mermaid bakery vanilla butter cake along with extra milk. It is a scratch cake. I've attached the link to the recipe - the addition of the pudding and milk is mentioned in the comments. I'm going to try it next time I need one for work. I love the WASC, but I am trying to get some good scratch recipes that hold up to stacking, etc.
http://cakecentral.com/recipes/4313/vanilla-butter-cake-from-the-mermaid-bakery
I am going to try adding a box of pudding to the "A Better Scratch White Cake" recipe. I thought that cake had a great flavor, but was just a little dry and crumbly to me.
I have never tried pudding but I am.
to your box mixes
add an extra egg to what it calls for
instead of water add whole milk and add 1/4 cup more
and beat beat beat
Cake is moister and rises better
It's just for cake mixes. NEVER add to a scratch recipe.
I happen to have a recipe for a scratch pound cake that calls for a small box of vanilla pudding. It is the most moist, excellent pound cake I have ever had. It made me think twice about adding a box to other scratch recipes. I just have not tested it out, yet.
Okay, well then that recipe was designed for the pudding mix. Scratch recipes are finely balanced. Adding pudding mix to recipes that aren't designed for it result in a gummy cake. I know. I've tried it. Honestly, scratch recipes don't need it in there. If you don't think a scratch recipe is moist, either you've run across a bad recipe (they are out there) or you've messed up somehow.
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