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John Wooden led UCLA Basketball to 88 straight wins in the early 1970s.
When the UCLA Bruins defeated UC Santa Barbara 74-61 on January 30, 1971, nobody had any idea how long the Bruins would keep winning for. They would win the remainder of their games that season, concluding by defeating Villanova for the NCAA Championship.
The next year, they would again go undefeated, ultimately beating Florida State for the NCAA title. In the end, they would not lose again until January 19, 1974, when they lost to the Notre Dame Fighting Irish 71-70. Notre Dame had also been the last team to defeat the Bruins prior to the streak beginning.
It should be noted, however, that the Bruins had a much easier road to the wins than these Huskies have. Their regular season schedule was not nearly as strong as the Huskies' has been. Although the Huskies have played (and dominated) multiple Top 10 teams along the way as part of their non-conference schedule, UCLA played largely against opponents in the Western United States. At the time, the west was the weakest basketball area, and the Bruins basically could pick almost any basketball prospect they wanted, if not west of the Mississippi, then at least west of the Rockies. Today, even in the women's game, the Huskies at least face some competition from schools like Tennessee, Stanford, and Notre Dame for prospects.
Also, at the time, the NCAA tournament "regionals" actually were regional, which means as a team from the west, UCLA had a much easier time winning. In 1972, for instance, the Bruins came out of the Western regional and defeated Weber State and Long Beach State on their way to the Final Four. Florida State, out of the Mideast regional, was forced to defeat Eastern Kentucky, Minnesota, and Kentucky before reaching the Final Four.
Due to the expansion of the NCAA Tournament over the last 40 years, there are a lot more "weak" teams in the field, but even still, the Lady Huskies managed to defeat tough teams from Iowa State and Florida State in the regional semifinals and final respectively (UCLA effectively started in the Round of 16, so comparing results from earlier in the tournament than that is tough).
Nevertheless, it was still a very impressive streak for the Bruins and for coach John Wooden. It is also worth noting that Notre Dame is the Big East team most likely to end UConn's streak in the forseeable future. The Huskies play at the Irish on January 8th. If they can get past a road game at Stanford 10 days earlier, that will prove to be the next challenge for the Huskies.