(covers information from several alternate timelines)
An accent was a vocal inflection particular to the people in a specific geographical region.
In 2152, a Risan woman told Hoshi Sato that she spoke the Risan language with hardly any accent. (ENT: "Two Days and Two Nights") Feezal Phlox also noticed the same thing when Sato spoke Denobulan. (ENT: "Stigma")
Also that same year, Soval noticed that T'Pol had developed a slight Human accent. (ENT: "Cease Fire")
In 2154, Arik Soong speculated that, based on his hearing of Trip Tucker's accent, the Orions were similar to Human ancestors. (ENT: "Borderland")
In both the prime reality and the alternate reality, Pavel Chekov's Russian accent caused him to pronounce "V"s as "W"s and vice versa. A passerby had difficulty understanding Chekov who was looking for "nuclear wessels" in Alameda. (Star Trek IV: The Voyage Home) The computer of the alternate reality USS Enterprise could not entirely distinguish between accented speech and a mistake in a spoken authorization code, much to Pavel Chekov's frustration. (Star Trek)
In 2259 of the alternate reality, Carol Marcus spoke with a British accent, though her prime reality counterpart did not. (Star Trek II: The Wrath of Khan; Star Trek Into Darkness)
In 2269, Nurse Christine Chapel mimicked Montgomery Scott's Scottish accent while praising his Bedside manner with Mira Romaine. (TOS: "The Lights of Zetar")
Lwaxana Troi commented in 2364 that her daughter's accent sounded much like that of Deanna's late father, Ian Andrew Troi. (TNG: "Haven")
In 2369, multiple holographic characters from an Ancient West holoprogram (which, due to a computer glitch, took on the appearance of Data) exhibited different accents, including Western and Mexican. (TNG: "A Fistful of Datas")
In 2372, Vedek Porta complimented Benjamin Sisko on his improving accent when speaking in the Bajoran language. (DS9: "Accession")
In 2374, Vic Fontaine removed the Russian accent from Julian Bashir's holographic character Lola Chrystal – a feat which took over an hour – to allow Odo to pretend she was Kira Nerys. (DS9: "His Way")