Good stuff right here.
Especially at the end.
UNC
NCAA Tournament Champions
1924, 1957, 1982, 1993, 2005
NCAA Tournament Final Four
1946, 1957, 1967, 1968, 1969, 1972, 1977, 1981, 1982, 1991, 1993, 1995, 1997, 1998, 2000, 2005
Conference Tournament Champions
1957, 1967, 1968, 1969, 1972, 1975, 1977, 1979, 1981, 1982, 1989, 1991, 1994, 1997, 1998, 2007
Conference Regular Season Champions
1956, 1957, 1959, 1960, 1961, 1967, 1968, 1969, 1971, 1972, 1976, 1977, 1978, 1979, 1982, 1983, 1984, 1985, 1987, 1988, 1993, 1995, 2001, 2005, 2007
The Tar Heels own several of the most impressive streaks in college basketball history. They appeared in either the NCAA Tournament or National Invitation Tournament (NIT) every year from 1967 to 2001--including 27 straight appearances in the NCAA tourney from 1975-2001 (the all-time consecutive appearance record) after that competition allowed more than one team from a conference to get a guaranteed bid. Arizona is second to the Tar Heels with a current streak of 23 NCAA Tournament appearances (longest active streak). The Tar Heels also did not have a losing season from 1963 to 2001--the third-longest such streak in NCAA history, second only to UCLA and Bowling Green, who has only made the NCAA tourney 4 times but has made the NIT 53 times since 1950.
From the ACC's inception in 1953 to 2001, the Tar Heels did not finish worse than a tie for fourth place in ACC play. From 1965 onward, they did not finish worse than a tie for third, and from 1965 to 1986 they did not finish worse than a tie for second. Neither of these streaks have been seriously threatened by another ACC team; during this time the ACC's other six charter members finished first at least once and last at least once, and only Clemson failed to win a tournament title.
All of these streaks ended in the 2001-02 season, when the Tar Heels had a dreadful 8-20 season, the worst in school history. They also finished tied for 7th in conference play, behind Florida State and Clemson--their second losing conference record ever (the first being in the ACC's inaugural season).
Additionally, the Tar Heels hold an interesting and possibly unique record in terms of a recurrent head-to-head rivalry. In 53 tries, Clemson has never beaten UNC in men's basketball in a game that was played in Chapel Hill. (The only possible longer streak is Princeton's home dominance of Brown, which stood at 52 straight wins as of 1/14/2003.)