The phrase "countless varieties of" is correct and usable in written English.
You can use it when referring to a large number of different types or kinds of something.
Example: "There are countless varieties of apples available at the market, each with its own unique flavor and texture."
Alternatives: "numerous types of" or "a multitude of varieties of".
The lean, lunging music is matched to gimlet-eyed observations about the countless varieties of betrayal.
Garden centres offer countless varieties of Berberis thunbergii, with fiery autumn foliage setting off a mass of bright red berries.
But there are countless varieties of fragrant rose, everything from garden favourites Rosa gallica and R. damascena to R. rugosa.
Mr. Kechiche trains his camera tightly on both actresses, using countless varieties of close-ups to track every flicker of feeling on their faces.
At the Village Underground last Thursday night, she sang about longing, temptation, sin and post-breakup loneliness, probing the countless varieties of heartache.
Dr. Harriman says that once the outcry over genetic engineering subsides, Scotts and other companies will will churn out countless varieties of grasses and ornamental flowers.
Although it may seem, especially to philosophers, that word usage is determined by the application of distinct and definite rules and thus that knowing the meaning of a word is the same as knowing the corresponding rule careful examination of actual speech situations shows that in no case can a single rule account for the countless variety of uses to which an individual word may be put.
A countless variety of animals might have existed, which do not exist.
Brown who as the Sceptred Isle's chief financial officer had boosted a countless variety of taxes–had been thinking of calling an election this month.
From sweet to savory, there is a countless variety of street food ranging from one region to the next.
One can drink the same sourish local wines in the taverns on the outskirts of town, consume the same mountains of whipped cream at Sacher's and Demel's, and sample the same infinite varieties of coffee in countless cafés.
