Dr. Horrible's Sing-Along Blog (live-action web miniseries)
Premiering in 2008, the miniseries is an original story, with songs composed by Joss, Zack, and Jed Whedon, and Maurissa Tancharoen. And it is awesome. I might even go so far as to call it legendary.
Hamilton (live-action film)
Premiering in 2020, this is a filmed performance (or composite performances filmed in 2016) of the 2015 stage play, with music composed by Lin-Manuel Miranda. It was originally intended to be released theatrically, but instead debuted on the Disney+ streaming service.
I Am With You (animated webseries episode)
Premiering in 2020, this is an episode of the webseries At Home with Olaf. It features an original song written by Kristen Anderson-Lopez and Robert Lopez.
LearningTown (live-action web series)
Premiering in 2013, the series features songs by Paul Sabourin & Storm DiCostanzo. Some of the songs occur naturally, since the characters are singers, but many of them definitely occur in ways that can only happen in a musical.
Les Miserawesomes (animated webseries episode)
Released in 2015, this is an episode of The Awesomes, where most of the team and pretty much everyone in France is forced to sing everything (badly) after drinking mind-controlling wine.
Les Neilérables (live-action webseries episode)
Released in 2009, this is an episode of The Legend of Neil where all the characters were singing because why the fuck not, I guess. (Really, there's no explanation. But it was fun.)
Mary Poppins Quits (live-action webisode)
Premiering in 2014, this is a short spoof of the 1964 film Mary Poppins. It was written by Eliza Skinner and Jake Fogelnest.
My Little Pony: Equestria Girls - Legend of Everfree (animated film)
Released in 2016, this is the fourth movie in the Equestria Girls franchise, and the first one to be released on Netflix rather than Discovery Family (at least in the U.S.). Like the first three films, it has original songs composed by Daniel Ingram.
Princess Rap Battle (live-action webseries)
Premiering in 2014, this isn't a musical per se, but the whole point of each episode is a song. Generally it involves Disney princesses, or at least that was the original idea. But it can include pretty much any fantasy or sci-fi female characters. The show is written, produced, directed by, and stars, Whitney Avalon.
Stars Hollow: The Musical (live-action web miniseries scenes)
Premiering in 2016, the "Summer" installment of "Gilmore Girls: A Year in the Life" includes scenes from a musical about the history of the fictional town Stars Hollow. Original songs were written by Amy Sherman-Palladino and Daniel Palladino, with music written by Jeanine Tesori.