Quoted By:
Kanto-Orange Islands Era
discounting Pikachu Ash caught 11 Pokemon (12 if you count Raticate, but I'm not here)
Of those 11, 5 were single-stagers or fully evolved upon capture.
of the remaining 6, 4 evolved to their final stages
leaving 2 unevolved Pokemon in this time period
Johto
Ash caught 6 Pokemon in this time
Of those 6, 2 were single-stagers or fully-evolved at capture
of the remaining 4, 1 reached its final stage and 2 evolved once
leaving 1 unevolved Pokemon from this era
Hoenn
Ash caught 6 Pokemon
Of the 6, 1 was a single-stager (technically 2, because Aipom was at the time it was caught)
Of the remaining 5, 3 reached their final stage
This would leave 2 unevolved Pokemon from this era, as Aipom evolved after she was traded to Dawn.
Sinnoh
Ash, again, caught 6 Pokemon
Of the 6, none were evolved or single-stagers at capture
4 of the 6 reached their final stages
again, leaving 2 unevolved
Unova
Ash caught 9 Pokemon
of the 9, 2 were evolved at capture, none fully, and no single-stagers.
3 Pokemon reached their final forms, and two evolved once.
leaving 3 unevolved Pokemon in this era
So in his career as a trainer, Ash has owned 39 total Pokemon counting Pikachu.
of the 39, 8 were single-stagers or fully evolved at capture
1 was evolved at capture that didn't reach its final form
15 reached their final form
4 evolved once
leaving 11 total pokemon that never evolved in Ash's care. That's a touch over 25%. Draw from that what you will.