The Globe has just set up its own TV player, from which you can rent or own productions of pretty much every Shakespeare play (I make it 35 out of 38,I think the three missing ones are those not in the First Folio, but I admit I haven’t double-checked*). Check it out here. I think the idiosyncratic choice of languages is down to their 2012 programming (as part of the Cultural Olympiad they produced every Shakespeare play, but using theatre companies from around the world), and the relative newness of producing digital versions, rather than reflecting a conscious decision. It’s good to know that I can watch Cymbeline, even if it is in Juba Arabic.
In terms of older productions, they have the Eve Best/Charles Edwards Much Ado About Nothing, which I really enjoyed live (it makes you realise how wasted he was in Downton Abbey), and Doctor Faustus starring Arthur Darvill, which may not be Shakespeare but I think will be well worth a look**. There go my plans for the weekend!
*I’m pretty certain – this is the professional scepticism kicking in.
** I saw him in Once earlier this year and it turns out he was totally wasted in Doctor Who