Different skills have different AD and AP scaling.
For example master Yi's alpha strike increases in power equal to 100% of your AP.
So building AP would increase that skill.
However, Garen on the other hand has his skills increased by attack damage.
So it depends on what champion you are playing and what how you want to play them.
Just note that Ability Power does not increase the power of every ability so you need to know which ones do and don't.
Master Yi is a champion that I've seen been used AP and AD.
gaming.stackexchange.com/users/22196/Andrew Henry
Ehhhh...
Honestly?
Depends on the champion.
More specifically, it depends on if any f their abilities key off of AP, and how strongly.
For example, AP Yi is doable, AP Garen is not.
Because none of Garen's moves have any AP Ratios (To my knowledge).
Do some research on Leaguecraft.com or other sites about your favorite champion's abilities!
:D
You'd be surprised!
Have fun!
gaming.stackexchange.com/users/22189/Mattarias
Abilities are a tricky thing but you can easily tell from the in-game tooltip.
If you see a +X on the damage amount for a skill show up in green text then it scales off AP.
If you see it show up in orange text then it scales off AD.
Some scale off both, like some of Miss Fortune and Katarina comes to mind.
Auto-attacks (Right-clicking) on champions is only based off AD damage.
However, auto-attacking structures (turrets, inhibitors, and nexus) are based off a combination of AD and AP.
A shortcut to get an idea of how to build or spec for a champion is to look at guides others have made.
gaming.stackexchange.com/users/22193/user22193
auto-attack heavy heroes benefit most by AD items but that does not mean that they wont benefit from AP items too
, it just means that the hero may benefit more from AD items due to the abilities scaling with AD and even those who scale with AP may not have high AP ratios and do not make the hero better than what it would be with AD items for an example an AP yi may have high burst and high healing due to meditate and alpha strike but that still gives him weaknesses such as the long time between the times he can use the abilities and even then if his meditate is interupted he becomes vulnerable to dying.
Where-as if he scaled AD he will be more useful due to his consistent damage, this does not make AP worse or better.
just some heroes are more useful as AD in more situations as they would as AP.
gaming.stackexchange.com/users/22270/Daniel Redford
AP does not boost auto-attacks at all , only AD does*.
*
In most cases anyways, very few champs get a small amount of bonus damage on auto-attacks based on AP.
Mainly due to their passives.
(See Diana, Orianna or Varus for examples)
Depending on the ability, the damage primarily scales with either AP (Green) or AD (Orange).
You can check this on each ability's tooltip.
the (+ ) will be color coded as any of the color's I've listed.
A small number of ability's can actually scale off of more than one source, and it will have two boxes [aka.
(+ )(+_) ]
with each being a seperate color.
There are few other rare cases where they are based on other factors.
One example is on max Mana (Blue, Ryze/Taric).
Other's are based off your max HP (Red, Volibear/Sejuani) and Armor (Yellow, Malph/Taric)
gaming.stackexchange.com/users/37612/VanBuzzKill
Champions like Garen, Miss Fortune and Master Yi have high physical damage and low magic damage, but with all of those champions, I use their abilities a lot.  This made me wonder, if I get AP items and runes does it increase those even more? Or do the abilities get stronger with AD items and runes?
Will AP items and runes help auto-attack heavy champions?
gaming.stackexchange.com
<league-of-legends>
gaming.stackexchange.com/questions/58254
gaming.stackexchange.com/users/22233/conjim
Different skills have different AD and AP scaling. Abilities are a tricky thing. AP doesn't boost auto-attacks. In League of Legends skills scale differently on each champion, depending on AP and AD or sometimes on other stats.
The community is giving an explanation how AP and AD scalling on skills work.