Before I was a huge film nerd, I used to be a Doctor Who nerd. Until I was 18, it was definitely the thing I was most a loser about. Anyway, I just learnt that the entire original run of Doctor Who is on Letterboxd. That is, the 1963 - 89 original 26 season run. Sadly, most episodes of the 2005 onwards revival are not on Letterboxd, so I didn't include them. I did include the 1996 TV movie though.
And yes, I have seen each and every one (though it's been quite a few years for many of them). The ones with episodes missing I have seen through reconstructions or animation, since the original audio does all survive.