Although not quite as old as the FA Cup itself, the Welsh Cup remains one of the oldest national association football cup competitions in the world, dating back to 1877 and contested every year since. (Except when the British were saving the world from German domination of course.)
Readers with a grasp of British geography will note that a number of the finalists in the competition are not located within what is customarily regarded as the borders of Wales. It should be noted that Oswestry for example, has always been a member of the Football Association of Wales and as such is a 'Welsh' team despite its geographic location. (In much the same wasy as Berwick Rangers is a 'Scottish' team despite the fact that Berwick on Tweed is in England). But it was also a tradition for many of the 'border' clubs such as Chester, Hereford United or Shrewsbury Town to regularly compete and re-enact the border conflicts of old, and sally forth against Welsh opposition and even occasionally bring home a piece of silverware for the trophy cabinet.
From the 1961-62 season onwards the victors qualified to play in the European Cup Winners' Cup, except of course the winner was an English club, in which case the losing Welsh finalist got to play (despite losing). This generally meant that one of the top Welsh clubs such as Cardiff, Swansea or Wrexham got to try their luck against the likes of Real Madrid and Dynamo Kiev despite their lowly second or third division status within the Football League.
The entire character of the Welsh Cup was changed in the 1995/96 season following a decree by UEFA that access to European competitions would be barred unless the Welsh Cup was restricted to teams in the Welsh league structure. Not only did this mean that no more would the likes of Kiddermister Harriers be able to seek fame and cup glory in a few cross-border raids, it also meant the exclusion of all the Welsh teams playing in the English league structure.
Therefore from 1995/96 onwards the Welsh Cup became a more muted affair.
The winner stil gets to play in Europe in the UEFA Cup (which replaced the European Cup Winners' Cup after 1990) although now the winners are one of the top League of Wales clubs, who generally get to play a qualifying round or two against top Latvian or Lithuanian opposition.
The Welsh Cup
Winning and Losing finalists since 1877
Information on past winners sourced from the Rec.Sport.Soccer Statistics Foundation website at http://www.rsssf.com/nersssf.html confirmed by data at http://www.citizens-choice.co.uk/WelshCupWinners.htm