Which country invaded Wales?

Principally England- parts of it were occupied by the Romans, but they weren't able to hold all of it, and only succeeded in remaining there at all by striking up peace treaties with regional warlords.
The Welsh succesfully kept the Saxons out following Roman withdrawal and the gradual invasion and settlement of England during the First Millennium by the Angles, Jutes, Saxons and Vikings. But they suffered heavily following the Norman Conquest of 1066- the Normans were hard-pressed to subdue the Welsh in the 200 years that followed, but following the death in action of Llewellyn the Great in 1285 (the only Welsh king to have truly succesfully united his country) they embarked upon a massive castle-building programme to keep wales under heavy military occupation.
The rebellion of Owain Glyndwr in 1400 threw English domination out and established Wales as an independent nation for 10 years, but this was finally crushed by Henry V in 1410. Thereafter, Wales remained under the English jackboot for nearly 550 years and was in fact amalgamated as PART of England under the Act of Union in 1536 (ironically passed by King Henry VIII, who was himself half-Welsh). It was only re-established as a seperate entity in Edwardian times, and it's flag has never been incorporated into the Union Jack.

From the 1960s onwards, Welsh nationalist activity and the formation of the 'Free Wales Army' (the Welsh equivalent of the IRA) has led to an increase in freedom for the nation. It now has it's own autonomous Assembly that controls all Welsh law except policing and criminal justice- however, hostility to Welsh autonomy remains rife in the English media, and you will never find fair and impartial coverage of Welsh affairs from the BBC or in English broadsheet newspapers.

During the first Millenium, Wales was also sometimes at war with Ireland, but in those days Wales was by far the more powerful military force and actually occupied the Central East part of Ireland for a long time, including the area that now incorporates modern-day Dublin. Relations between Wales and Ireland have always been volatile at best- many Irish dislike the Welsh more than they do the English, and the IRA only refrained from bombing Wales because it would not have attracted sufficient media attention rather than out of any sense of Celtic brotherhood.