The most common area is music - crescendo, adagio, legato... and so on - although for reasons that escape me we mispronounce mezzo-soprano (English speakers insist on using /ts/, where the Italian has a clear /dz/). And a lot of users use crescendo as if it meant 'peak in a loud sound' (*"the hubbub rose to a crescendo") rather than 'getting louder'.
There's food, of course: spaghetti (although English speakers gloss over the double T) rissotto (ditto), pizza and so on. Some foods are pronounced with a French influence: a lot of people pronounce lasagne (three syllables in Italian) with two syllables (and a /z/). Spelling is also sometimes influenced: we have adopted panini (although in English it's usually singular - although I can't bring myself to say 'a panini', so I often just point); but sometimes, using the English spelling rule that doubles a consonant to keep a vowel short (ban/banning versus pave/paving), people spell the new word "pannini" (I've seen this painted on a shop window, which suggests it's not a casual typo).
There's also a very odd one - which doesn't exactly borrow the Italian word. A decorative but vapid 'trophy' escort* is a 'bimbo' (with an O), although a baby girl (compare 'babe' in Am English) is bimba**.
PS *female, that is
** In Italian, that is
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