There's a few, but those that come to mind off the top of my head are:
Pupitar – Tyranitar: Loses the Ground typing and gains the Dark typing.
Skorupi – Drapion: Loses Bug typing and gains the Dark typing.
Eevee – Jolteon / Flareon / Vaporeon / Espeon / Umbreon / Leafeon / Glaceon / Sylveon: Loses Normal typing and gains the Electric, Fire, Water, Psychic, Dark, Grass, Ice or Fairy typing, respectively.
Nincada – Ninjask / Shedinja: Loses the Ground typing and gains the Flying or Ghost typing, respectively
Onix – Steelix: Loses the Rock typing and gains the Steel typing.
Scyther – Scizor: Loses the Flying typing and gains the Steel typing.
Surskit – Masquerin: Loses the Water typing and gains the Flying typing.
Azurill – Marill: Loses the Normal typing and gains the Water typing.
Swablu – Altaria: Loses the Normal typing and gains the Dragon typing.
Kirlia – Gallade: Loses the Fairy typing and gains the Fighting typing.
Fletchling – Fletchinder: Loses the Normal typing and gains the Fire typing.
Skrelp – Dragalge: Loses the Water typing and gains the Dragon typing.
Also note that Gloom loses the Poison typing when evolving to Bellossom, but does not gain an additional type, remaining pure Grass.