I was bored, so I put this together in about half an hour.
Basically, this is a list of the possible combined burst damage/healing of all champions.
There are some heroes that just cannot have a definite ratio, and they have notes next to them.
This shows how well each champion scales with ability power when their role is burst dps. Nothing more, really.

When possible, it is assumed that this is under the best circumstances (i.e. Corki's Valkyie hits for the entire duration).

Alistar- 2.4
Alkali- 2.6 (in addition to her passive)
Amumu- 2.375
Anivia- 2.25
Annie- 1.9
Ashe- 1.0
Blitzcrank- 2.05
Cho'Gath- 2.4
Corki- 4.1
Dr. Mundo- .2 (per second)
Evelynn- 1.28
Ezreal- 2.35
Fiddlesticks- 4.5 - 7 (Dark Wind varies)
Garen-None
Gragas-1.9
Gangplank-1 + (0 to 5.6 for Cannon Barrage)
Heimerdinger- 2.35 + (.25 * number of turrets attacking enemy * seconds spent attacking)
Janna- 3.75
Jax- 2.3
Karthus- 1.65
Kassadin- 1.9
Katarina- 3.75
Kayle-1.95
Kennen- 2.66
Malphite-1.6
Malzahar-3.1
Master Yi- 2.65
Morgana- 5.2
Mordekaiser- 1.55
Nasus-1.2
Nidalee-2.35
Nunu- 4.5
Pantheon- 2.0
Poppy- 1.4
Rammus- 3.4 ( + .25 for each enemy attack)
Ryze- 3.55
Shaco- 4.0
Shen- 1.95
Singed- 1.3 (Anyone know how long the poison stays on the person for?)
Sion- 2.9
Sivir- 2.0
Soraka- 3.85
Taric- 3.4
Teemo- 2.3
Tristana- 3.1
Tryndamere- 2.5
Twisted Fate- 1.2
Twitch- 1.0
Udyr- 1.75
Veigar- 2.8
Warwick- 1.0
Zilean- 4.1

Top 3
Fiddlesticks - 4.5 - 7 (dark wind varies)
Morgana - 5.2
Nunu - 4.5

Bottom 3
Garen - 0
Twitch - 1.0
Warwick - 1.0

Major Credit to Motas. He provided all abilty ratios.

It would be nice if this were stickied so it doesn't get lost. I'll update this with new patches.

You didn't count consume?

Sorry, forgot it also healed him.

Maybe. I don't think so though, because its .2 per second, so if he has it on for more than 5 seconds, it has a better ratio than WW or twitch. I haven't played mundo though. Does that usually happen?

fix'd

This is single target damage, so I'm not counting the additional enemies katarina hits with her ult.

According to Motas's thread, Katarina throws twelve daggers, which means .3 * 12 = 3.6. +.75 =4.35. Did he not update it correctly though?

Akali
Q: .4 + .4
E: .3
R: .5
Total: 1.6

Passive makes the first 20 AP give an extra 11 damage per auto attack with no + dmg items.