Shea, Sveta, Caroline Doty, Morgan Tuck, Brianna Banks -- and unfortunately we need to add Sue Bird to that list, going down in her freshman year. What made that loss even worse was that since she had played in more than 20% of the team's games that season (1998-1999), she was not allowed to redshirt.
Her TASSK Force teammate, Keirsten Walters, never did realize her potential due to injuries.
And if I recall correctly, Nicole Wolff also had chronic injury issues and redshirted a year (however, she chose to graduate with her classmates).
Jessica Moore and Ashley Battle had to heal and come back from injury. Jess (in)famously tore her ACL in one of the championship games against Tennessee, but finished the game with 14 points and 9 rebounds; while Ashley's elbow injury in her freshman year resulted in a redshirt.
Just my opinion, but I think UConn has had its share of injuries over the years. Overall, we're not quite as lucky as some may think.