I can think of three possibilities. First, certain words from one language might not have an acceptable match in another language. So you might have a word in one language that has a certain meaning or tone or slant to it, and there may be no word in the language you are translating to that comes close to conveying what is meant. Second, there is the possibility that a term is not translated because the term has an accepted role as part of specialist language (as, for example, when a philosopher uses a Latin term when speaking to an audience that probably doesn't know much Latin, but who probably understand the meaning of a handful of Latin terms... cogito ergo sum, for example). And third... the Trek writers and producers just think it sounds cooler to throw in some strange words here and there.
Fourth: They're doing it manually. Why wouldn't they be able to disable the translator as they please? We know that some characters know how to speak some alien languages. It may be preferable to not use the translator if possible, so when dealing with people with which they've had a long history and time to learn their language, such as Klingons and humans, they (the Klingons) simply speak English, or vice versa.
Fifth: Isn't the Universal Translator generally only in use for intership communications? I can think of plenty of times that crew members have looked to Data for translations. By Deep Space Nine, there are universal translators(located in the Ferengis' ears) which are broken and need to be fixed before Quark can communicate with the humans. (Little Green Men)
Sixth: Obscene words often are not translated.
Real world reason different languages can be used as plot device.