I call those unit target spells, which can deal damage to their target in only one damage instance, no matter whether they have a projectile or a damage delay, the "direct damage" spells.

There are 65 "direct damage" spells currently. They are:
Abaddon Mist Coil
Alchemist Unstable Concoction Throw
Anti-Mage Mana Void
Axe Culling Blade
Bane Brain Sap
Beastmaster Primal Roar
Bounty Hunter Shuriken Toss
Broodmother Spawn Spiderlings
Centaur Warrunner Double Edge
Dagon Energy Burst
Dragon Knight Dragon Tail
Earth Hurl Boulder
Earth Spirit Boulder Smash
Earth Spirit Enchant Remnant
Enigma Malefice
Ethereal Blade Ether Blast
Eul's Scepter of Divinity Cyclone
Gyrocopter Homing Missile
Harpy Stormcrafter Chain Lightning
Huskar Life Break
Invoker Cold Snap
Iron Talon Chop
Leshrac Lightning Storm
Lich Chain Frost
Lich Frost Blast
Lina Dragon Slave
Lion Finger of Death
Luna Lucent Beam
Medusa Mystic Snake
Morphling Adaptive Strike (Agility)
Mud Golem Hurl Boulder
Nature's Prophet Wrath of Nature
Necrophos Reaper's Scythe
Night Stalker Void
Nyx Assassin Mana Burn
Ogre Magi Fireblast
Ogre Magi Unrefined Fireblast
Oracle Fortune's End
Oracle Purifying Flames
Outworld Devourer Astral Imprisonment
Phantom Lancer Spirit Lance
Queen of Pain Shadow Strike
Riki Blink Strike
Rubick Fade Bolt
Satyr Mindstealer Mana Burn
Shadow Demon Demonic Purge
Shadow Shaman Ether Shock
Silencer Last Word
Skywrath Mage Arcane Bolt
Sniper Assassinate
Spectre Spectral Dagger
Spirit Breaker Nether Strike
Sven Storm Hammer
Tidehunter Gush
Tinker Laser
Tiny Toss
Tusk Snowball
Tusk Walrus Kick
Undying Soul Rip
Vengeful Spirit Magic Missile
Visage Soul Assumption
Witch Doctor Paralyzing Cask
Wraith King Wraithfire Blast
Zeus Arc Lightning
Zeus Lightning Bolt

Furtherly, there are 15 unit target spells using damage with a more complex formula than others.
They are:
Alchemist Unstable Concoction Throw
Anti-Mage Mana Void
Centaur Warrunner Double Edge
Ethereal Blade Ether Blast
Huskar Life Break
Iron Talon Chop
Lion Finger of Death
Morphling Adaptive Strike (Agility)
Necrophos Reaper's Scythe
Nyx Assassin Mana Burn
Satyr Mindstealer Mana Burn
Silencer Last Word
Skywrath Mage Arcane Bolt
Undying Soul Rip
Visage Soul Assumption

Note:
1. Since Chaos Bolt deals a random damage, it should not be considered.
2. Although Shadow Strike applies a debuff which deals damage over time, it deals a direct damage which is not same as the dot.

I suggest adding a damage indicator, which shows the damage (before any reduction) of the spell, right after the player clicks the spell and hover the mouse cursor over its target. The damage indicator could be a grey or darker area on healthbar, or simply a number anywhere around its target.

Note:
1. Some of above can target ally or ground. when do so, damage indicator is not shown.