From what I see here it looks like 18 are learned without requiring dragon souls, though I'm extrapolating a bit since I haven't reached the end of the main quest yet, myself.
Fuzzy math:
Animal Allegiance 3 Souls
Aura Whisper 3 Souls
Become Ethereal 3 Souls
Call Dragon 0 Souls*
*I'm making the assumption that this works a bit like Unrelenting Force
Call of Valor 0 Souls
Clear Skies 0 Souls
Disarm 3 Souls
Dismay 3 Souls
Dragonrend 0 Souls
Elemental Fury 3 Souls
Fire Breath 0 Souls
Frost Breath 3 Souls
Ice Form 3 Souls
Kyne's Peace 3 Souls
Marked for Death 3 Souls
Slow Time 3 Souls
Storm Call 3 Souls
Throw Voice 3 Souls
Unrelenting Force 1 Soul
Whirlwind Sprint 0 Souls
So...3+3+3+0+0+0+3+3+0+3+0+3+3+3+3+3+3+3+1+0 = 42
