Ash's Fully Evolved Pokemon:
Staraptor (On hand)
Gliscor (On hand)
Kingler (With Professor Oak)
Muk (With Professor Oak)
Tauros (x30)(With Professor Oak)
Snorlax (With Professor Oak)
Heracross (With Professor Oak)
Noctowl (With Professor Oak)
Donphan (With Professor Oak)
Sceptile (With Professor Oak)
Torkoal (With Professor Oak)
Swellow (With Professor Oak)
Glalie (With Professor Oak)
Primape (With Anthony)
Charizard (In Charicific Valley)
Butterfree (Released to breed with Pink Butterfree)
Pidgeot (Released to protect flock of Pidgey and Pidgeotto)
Lapras (Released back to its pod)
Beedrill (Gave it to Casey)
Ash's Unevolved Pokemon:
Pikachu (On hand)
Grotle (On hand)
Monferno (On hand)
Buizel (On hand)
Bulbasaur (With Professor Oak)
Cyndaquil (With Professor Oak)
Bayleef (With Professor Oak)
Totodile (With Professor Oak)
Corphish (With Professor Oak)
Squirtle (With the Squirtle Squad)
NOTES:
1. I'm not counting any Pokemon which Ash traded away if he got a Pokemon in return for the trade.
2. I'm not counting any Pokemon which Ash be-friended or borrowed/rented.
Anyway, as you can see Ash has more fully evolved/one-stage Pokemon than he does have a Pokemon which is unevolved. In addition Ash only have 10 unevolved Pokemon and they are indeed atleast part Grass-, Fire-, or Water-type such as edmasterchaos.
And responding to edmasterchaos's post:
* I'm going to assume you mean you want Snorlax to have an evolution as it does have a pre-evolution, Munchlax.
* Misty has a Psyduck which can evolve into a Golduck, once it was mistaken to have evolved into one once.