Based on some rather fuzzy math: 44
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 - 2 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 - 2 Souls
So...3+3+3+0+0+0+3+3+0+3+2+3+3+3+3+3+3+3+1+2=44
