First off, don't call a Traveller a "Gypsy." It's a derogatory word, and just about the most offensive way you can possibly refer to an Irish Traveller. Only the word "pikey" might be worse, but that only happens in Britain. "Knacker" is another well known derogatory term. Some Travellers today are significantly more offended by "knacker" than "gypsy". Older works might call them "Tinkers," from the fact that a lot of them used to be itinerant tinsmiths. This is also considered offensive, if not so much. The proper word is "Pavee," not that you'll hear it used much.
Irish Travellers are a people who share the language Shelta, commonly known as Cant, derived from a mixture of intentionally-incomprehensible Irish slang and a few English, Romani, and other loanwords. They are tribal, like the Romani, and share the perception in media as being "evil outsiders", like the Romani, and some are nomadic, like some Romani, but that is it.
The fact that Irish Travellers are culturally different from most other White Europeans—including other ("Settled") Irish—is where a lot of the media bias comes from.
In Britain, Irish Travellers are legally considered a separate ethnicity from the settled Irish community. In Ireland, they are not. This is why references in Irish media are made to 'the Travelling community' and 'the Settled community'. All of this a political hot potato.
There is a population of about 7,000 Travellers in the United States, concentrated in the Deep South. Some have settled down, but others still maintain the Travelling lifestyle, albeit in RVs rather than the more traditional covered wagons.
The Mad Scientist Wars suggests that one of Andrew Tinker's Mad Scientist grandfathers, Dr. Io, is an Irish Traveller. It hasn't been gone into too much, but Dr. Io is presented as a kind, good person, so it's a positive portrayal.
Chocolat has a band of Travellers living in riverboats, whose leader is played by Johnny Depp. They are discriminated against by the townspeople and the conservative mayor denounces them as godless and a bad influence. The protagonist strives to overcome this prejudice, in accord with her role as the Blithe Spirit. In the book the film was based on, where the person inveighing against the Travellers is the local ultra-conservative priest, who basically rules the town through fear until the protagonist shows up, so his denunciations of godlessness have more force to them. Also, he sets fire to all of the Travellers' barges—twice. Even the chapters from his point of view, when contrasted with what the reader actually knows about the Travellers, show his bigotry to be hysterical, irrational and dead wrong.
In Snatch, a clan of Travellers (and their champion bareknuckle fighter in particular) plays a big role. They're all liars and con-men, but so is every other character in the film. It's a Guy Ritchie movie; if there's a moral high ground, the Travellers are probably the ones occupying it, especially considering that they're up against a London Gangster.
Into the West, a Magical Realism story about two Traveller boys escaping from the grimness and poverty of early '90s Dublin.
Pavee Lackeen (which is Cant for The Traveller Girl) is a pseudo-docu-drama about a family of Travellers, the Maughans, who play versions of themselves coping with the everyday reality of being Travellers. It portrays them as well rounded people, but is by no means rose-tinted: it shows, among other things, children sniffing petrol, stealing clothes from charity bins, fighting in the street, etc. Alas, it's held back from being engaging by a complete lack of plot.
In The Field, a traveller woman shows up at a village dance and dares a man to "dance with the Tinker's daughter". She evenutally becomes the love interest of Tadgh.
In Stand Off (original title Whole Lotta Sole) Irish Travellers supply much of the humour and help to complicate the farcical proceedings. One of their children gets his head stuck between window bars and when the character played by Brendan Fraser uses soap to free him the boy does not know what it is.
There is a passing reference to Travellers in the novel The Book Of Kells by R. A. MacAvoy. John goes back to the present and sees a family in Dublin that look like they could be descendants of Ailesh and himself.
In Shirley Rousseau Murphy's Cat to the Dogs, some disreputable Travellers cause trouble for their less disreputable relatives.
In The Golden Compass (aka His Dark Materials), an alternate universe counter-part of the Irish Travellers are called gyptians (derived from the word "Egyptian," and oddly their lingo is referred to as "fen-Dutch," so presumably their ethnicity is a blend, half of the Gyptian charaters have Greek names, the other half have Dutch-sounding ones). They spend their time traveling the waterways of the British Isles play a large role in helping the protagonist Lyra as she searches for her lost friend (many of their own children having been taken as well). Some Travellers take such a shine to her that she is generally considered an unofficial member of their people. The word "Gypsy" is derived from a mistaken belief that the Romani people were descended from Egyptians. Thus, "gyptian" is probably an alternate-universe derivation along much the same lines.
This has some basis in our reality as well, as many Medieval Histories of Ireland and Scotland traced the Gaelic Peoples as a whole ultimately back to an Egyptian Princess [Scoti] in much the same way Britain was traced back to Brutus of Troy.
In Mary Beth Keane's The Walking People One of the main characters is an Irish Traveller. The Walking People is another name for Irish Traveller.
The Irish children's series by Kenneth Bird about a talking dog called Himself, whose owner is a tinker. The ongoing prejudice against tinkers is brought up several times in the series.
In the book Steadfast of the Elemental Masters series, Katie Langford is half-Traveller. Her dancer mother was the Traveller, and her acrobat father a non-Traveller man that was living a similar lifestyle. The two eloped when the Traveller clan refused to let the two marry, and Katie's mother was then cast out from the clan.
Law & Order: Criminal Intent: The murder at the heart of one episode was tied to an attempt to cover up a business deal between two families of Travellers. The deal being the arrangement of a marriage between two ten-year-olds so that a "dowry" could be exchanged to pay off some business debts.
One infamous episode of Star Trek: The Next Generation had Irish Travelers in SPACE via a group of "neo-transcendentalist" colonists known as the Bringloidi (Bringloid being Irish Gaelic for "dream"). They're about as stereotypical as you can get: slovenly, ignorant, and disruptive, led by a drunkard trying to marry off his nagging daughter. The script was approved by an Irish-American, but plenty of other Irish folks weren't amused.
Irish Travellers are very much a staple of Irish theater, from the 1908 comedy The Tinker's Wedding by J. M. Synge onwards. Marina Carr's By the Bog of Cats (1998) is probably the best known work internationally.