Hmm.
Hunter:
1 mana timber wolf = 0 damage
4 mana leeroy = 6 damage
2 mana unleash (guaranteed 2 hounds from leeroy) = 10 damage
3 mana kill command = 15 damage, 4 cards
If the opponent has minions, it'll be an extra 2 damage per enemy minion.
Mage:
2 mana sorcerer's apprentice = 0 damage
1 mana frost bolt = 3 damage
0 mana ice lance = 7 damage
0 mana ice lance = 11 damage
1 mana frost bolt = 14 damage
3 mana fireball = 20 damage
3 mana fireball = 26 damage, 7 cards
(arcane missiles x2: up to 32 damage, 9 cards)
Oddly enough, there are some mage decks that try to go for that big spell combo. You just need a lot of draw cards (acolytes, and that draw murloc, and loot hoarders). Then you just fill the rest of your deck with the necessary spells and filler.
Warlocks are a little difficult to predict because of the discarding. Leeroy + 1xPower Overwhelming, 2xSoulfire, faceless manipulator on leeroy. That would be 28 damage for 5 cards, + up to 2 discards. I've seen leeroy double overwhelming though--that is a bit more practical, and usually only one soul fire. You'll still end up with 18 damage.
Warrior:
3 mana raging worgen = 0 damage
3 mana charge = 5 damage worgen
0 mana inner rage = 8 damage worgen (windfury)
0 mana inner rage = 10 damage worgen (windfury)
2 mana rampage = 13 damage worgen (windfury)
2 mana rampage = 16 damage worgen (windfury)
Which would total 32 damage for 6 cards. Worgens are pretty fun. Rampage is situational, and so is charge. It is usually pretty difficult to get a combo like this.
Paladin:
3 mana wolf rider = 3 damage
1 mana blessing of might = 6 damage
1 mana blessing of might = 9 damage
5 mana blessed champion = 18 damage, 4 cards
Blessed champion is pretty strong since it is % based. I could see this maybe happening in a real game (with a weird deck). Alternatively, you can get lucky with a holy wrath by drawing a molten giant for 20 damage.
You can also replace 1 BoM and the wolfrider with leeroy.
Rogue:
4 mana Leeroy = 6 damage
1 mana cold blood = 10 damage
0 mana prep = 10 damage
0 mana cold blood = 14 damage
5 mana faceless manipulator = 28 damage
0 mana prep = 28 damage
0 mana eviscerate = 32 damage, 7 cards
I don't see faceless manipulator too often though. Usually it is just shadowstep into another leeroy. You can get pretty similar damage with it.
Priest:
4 mana stormwind knight = 2 damage
1 mana power word: shield = 2 damage
2 mana divine spirit = 2 damage
2 mana divine spirit = 2 damage
1 mana inner fire = 28 damage, 5 cards
Druid:
6 mana force of nature = 6 damage
0 mana innervate = 6 damage
0 mana innervate = 6 damage
2 mana murloc charger = 8 damage
3 mana savage roar = 18 damage
3 mana savage roar = 28 damage, 6 cards
Finish him off with two free moonfires, I suppose.
Shaman:
4 mana Leeroy = 6 damage
1 mana rockbiter = 9 damage
1 mana rockbiter = 12 damage
1 mana abusive sergeant = 14 damage
1 mana abusive sergeant = 16 damage
2 mana windfury = 32 damage
Mhm. It is fun to think about. It is never really that practical, but it can be fun for weird decks. In these, I ignored the possibility of coin and I ignored any preplaced units. There are some funner things you can do with preplaced units, though. e.g. Today I had antonidas and a sorceror's apprentice up. With a fireball in my hand, I ended up dealing 3 fireballs (18 damage) and 5 (archmarge) + 3 (sorceror's apprentice) for 26 damage.