How rare are the "rare biomes" in Minecraft?

The map in @UniversalElectricity's answer is from http://chunkbase.com/apps/biome-finder You can also enter seeds and find biome locations at http://mineatlas.com/ (note that for MCPE, these only work with positive seed numbers below 2 billion something.) Biome rarity depends on what it is next to. For example, Savannah spawns next to desert. Deserts can get very large, as can "temperate" biome collections. Some biomes are larger than others - ice plains can get large. Savannah, jungle, and Mushroom island are indeed very rare, but all biomes can usually be found within 8K - 10K blocks of spawn, most often closer. Some biomes are very common, even though they are small - forests, extreme hills, and plains are examples.

Mesa, mushroom, jungle, ice, and spruce are the rarest but we totally underestimate how easy it is to find one.

Example: Even in creative mode we might go forward flying looking for one but one slip of a finger can turn you right back around in survival one might run from mobs or turn to avoid a mountain and go in circles when one could be just up their another example as if you were in a jungle or mesa it would be just as hard to find dessert or grassland or savanna as I have spent hours in mesas and jungles trying to get out other rare biomes such as spruce and ice are literally tiny and it will be easy to find another biome other biomes will also take a long time to escape

Well personally the rarest biomes i have found are mushroom islands and Jungles, could never find either off them, then found them both yesterday! I spent most of my time on the boat to find cool biomes, including mesa which i recently found. Deserts are fairly common, and almost always have temples or sand villages. Hope this helped ;)