The word hippopotamus, denoting the large, gray mammal, comes from Latin (and thence from Greek), and its Latin plural is hippopotami. But hippopotamus is an English word when English speakers use it, and there is nothing wrong with pluralizing it in the manner of our own language: hippopotamuses.
Latin plurals are typically favored in scientific writing, however, and while some people who study animals use hippopotamuses in their own speech, the Latin plural is especially common in scholarly texts that mention the animal. In general usage, though, only a few Latin plurals are preserved by convention, and hippopotami is not common enough to be considered one of them.
Of course, anyone who wishes to get around the issue can go with the shortened hippos, which is actually more common overall than both of the others in this century.
The hippos had been just one of several “up close” encounters we had experienced that afternoon. [Telegraph]
“The state working group supported by Hanna called for a ban on private ownership of a specific list of animals, including panthers, hyenas, lions, tigers, primates, elephants, rhinoceroses, giraffes, hippopotamuses and crocodiles. [Columbus Dispatch]
The outlook is majestic and the river flowing nearby is home to a raft of hippos that make their presence known with loud snorts and grunts. [Sydney Morning Herald]
Colombian bounty hunters have shot and killed one of three hippopotamuses which escaped from a private zoo … [BBC]
Hunting in shoulder-deep water is all but impossible, and deadly hippos and crocodiles patrol the waters. [Independent Online]
The ngram below graphs the use of hippopotami, hippopotamuses, and hippos in English-language books published in the 20th century. It suggests that hippopotami was once the preferred form but has gradually given way to the others.