Many Many Many!
But the there are the basic 8 cloud types (Check Picture in the Answer for more details ;) )
The highest clouds in the atmosphere are cirrocumulus, cirrus, and cirrostratus. Cumulonimbus clouds can also grow to be very high.Mid-level clouds include altocumulus and altostratus.The lowest clouds in the atmosphere are stratus, cumulus, and stratocumulus.