Diamond, No Evolution or Breeding

The player can get up to 357 species total (395 with dual-slot encounters) in Diamond without trading, as described here. Without evolving or breeding any Pokémon, and only collecting evolutionary stages that the player can get in the wild, as a gift, or from an in-game trade, the player can get up to 241 species (269 with dual-slot encounters). Of the 357 possible species in Diamond, the Pokémon unavailable without evolving or breeding are as follows:

Starter Evolutions (2) - 2 total: The starters are only available in their base forms, leaving their evolutions inaccessible.
Stone Evolutions (22) - 24 total: Raichu, Nidoqueen, Nidoking, Clefable, Wigglytuff, Vileplume, Bellossom, Poliwrath, Victreebel, Cloyster, Exeggutor, Starmie, Vaporeon, Jolteon, Flareon, Togekiss, Sunflora, Honchkrow, Gallade, Delcatty, Roserade, and Froslass are inaccessible.
Breeding Pokémon (8) - 32 total: Without the ability to breed, Koffing, Ledyba, Spinarak, Wynaut, Poochyena, Taillow, Whismur, and Shuppet are inaccessible.
Fossils (5) - 37 total: The Fossils can only be revived into their base forms, leaving their evolutions inaccessible.
Other (79) - 116 total: Pidgeotto, Pidgeot, Crobat, Parasect, Persian, Rapidash, Magneton, Magnezone, Dodrio, Muk, Hypno, Kingler, Electrode, Marowak, Hitmonlee, Hitmonchan, Hitmontop, Lickilicky, Blissey, Jynx, Espeon, Umbreon, Leafeon, Glaceon, Snorlax, Dragonite, Furret, Togetic, Xatu, Ampharos, Azumarill, Sudowoodo, Jumpluff, Ambipom, Yanmega, Granbull, Weavile, Piloswine, Mamoswine, Mantine, Donphan, Pupitar, Tyranitar, Linoone, Cascoon, Dustox, Gardevoir, Masquerain, Breloom, Vigoroth, Slaking, Ninjask, Shedinja, Exploud, Hariyama, Probopass, Lairon, Aggron, Manectric, Swalot, Grumpig, Flygon, Altaria, Claydol, Milotic, Glalie, Metang, Metagross, Staraptor, Luxray, Wormadam, Mothim, Vespiquen, Cherrim, Drifblim, Lopunny, Gabite, Garchomp, and Lucario are inaccessible.
Dual-Slot Evolutions (10): Even if dual-slot encounters are allowed, Butterfree, Beedrill, Ninetales, Arcanine, Electabuzz, Magmar, Forretress, Gliscor, Ludicolo, and Shiftry still cannot be obtained.

Professor Oak(-ish) Challenge Notes

This just contains a list of areas you can find each Pokémon, ordered as though you are playing a Professor Oak challenge and therefore need to obtain every Pokémon as early as possible.

Pre-Badge 1 (Roark) - 13 Total Pokémon

Badge 1 through Badge 2 (Gardenia) - 35 Total Pokémon

Badge 2 through Badge 3 (Maylene) - 69 Total Pokémon

Badges 3 through 6 (Byron) - 79 Total Pokémon

Badge 6 through 7 (Candice) - 86 Total Pokémon

Badges 7 through Elite Four - 94 Total Pokémon

Post-Elite Four - National Pokédex - 241 Total Pokémon

All National Pokédex Pokémon are only available after defeating the Elite Four.

If the player has access to dual-slot capabilities, the following Pokémon can also be obtained:

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How Many Pokémon Can You Get Without Evolving or Breeding in Pokémon Diamond?