There are plenty of fictional sports teams that appear in movies and/or TV and, unsurprisingly, most of their designs suck. To me, a sports movie has to have real teams in it to add a true authentic feel. And even if a film can't afford the rights to the professional sports licenses they want to show, sneaking in a few 'illegal' jerseys or fan-made T-shirts can preserve the feel (see Big Fan's 'Dallas Sucks' T-Shirt as an example).
And if the movie isn't necessarily a sports film but a character loves sports or identifies with their area of birth or, in some cases, a particular film or television episode focuses on a sporting event, I like to see a true respect to detail by showing authentic, real team designs of all shapes and sizes (or something close to).
With no rhyme or reason, I decided to look at real, professional sports teams that have appeared in cinematic movies and television series since the dawn of those mediums. Some have entire motion pictures supporting them. Others get a passing reference through a worn shirt, an old hat, or a cameo guest spot.
I try to look at as many major and minor indications of sports franchises in cinema/television that I know of but, probably, and/or likely, I missed some or many. If you didn't see any that you particularly love, be it an entire movie or television episode, or just a loving and/or passing glance to a sports team that bears some significance to the movie/show/character, let me know in the comment section.