So i'll start by saying it feels like a somewhat stupid question in the sense that the answer is no, but im wondering if (for back story of races in a story) its realistically possible for a planet to just be majority or entirely one type of biome, i.e. desert, rain forest, wooded, snowy. it feels like no to me mainly because you end up with different climates due to the curvature of a planet and the distribution of warmth from a star. maybe the desert planet is constantly day time due to having multiple stars in its system, snowy i think is easy to justify, but rain-forest not sure honestly. So please do tear this thinking apart :)
Only one biome, no -- you need seas, or else there is no water cycle.
But markedly less climatic and biologic diversity than what we have now is indeed possible. Imagine Earth in the Cretaceous -- "a very gentle temperature gradient from the equator to the poles meant weaker global winds, which drive the ocean currents, resulted in less upwelling and more stagnant oceans than today" (Wikipedia). Temperate climate extended almost to the poles. If you don't have large continents there will be no deserts. So, minimum, sea, tropical, temperate.