Based on some rather fuzzy math: 42

From what I see here - http://www.uesp.net/wiki/Skyrim:Shout - 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 - 3 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 - 0 Souls

Unrelenting Force - 1 Soul

Whirlwind Sprint - 2 Souls

So...3+3+3+0+0+0+3+3+0+3+3+3+3+3+3+3+3+0+1+2=42