There are a lot of different names for these little birds in Spanish! If you just want a basic translation that could be used in any Spanish-speaking country, it's colibrí.
But you can also say:
pájaro mosca ("fly bird," "fly" as in the insect, because of its size)
chupaflor ("flower sipper," only used in Mexico and some other areas)
chuparrosa ("rose sipper," only used in Mexico)
chupamirto ("myrtle sipper," only used in Mexico)
picaflor ("flower piercer," especially used in South America)
zunzún (a word that imitates the sound they make; only used in the Caribbean)
gorrión (in Central America it means hummingbird but in Spain the same word means a different kind of bird)
chupamiel ("honey sipper," used poetically)
visitaflor ("flower visiter," used poetically)
joyas voladores ("flying jewels," used poetically)
me - bird lover and perpetual Spanish learner!