I had a Chase Slate card that was opened in '93, never used since '94, forgot about, and discovered was still open in '12. Had to close it at the beginning of this year, as the card had a 23.3K credit limit that was both in my wife's and my name (a joint account).
Could not apply for more Chase cards without closing it. Apparently since it was a joint account, the credit limit could not be lowered. Only choice was to close it completely. Kind of a bummer, since it had been open 19 years.
But hey, now I have several Chase rewards cards :-)