There are loads of "classics" I don't remember ever seeing, although I have been making a bit of an effort to watch more of the really old stuff, either on streaming, setting the Tivo to record when they're shown on BBC4, or picking up the DVD/Blu-ray cheap*. Every now and then I'll go through a phase of trying to watch as much stuff by a particular actor or director as I can, or films from a specific era and genre so for example watching British Sci-fi and horror from the 60's and 70's or American Slasher flicks of the 80's.
One problem I do keep running into is I keep getting diverted by the extras on a lot of the older films, as I'll be listening to a commentary or feature on the director and suddenly find myself looking through IMDB for other films they mention or some of the actors and what they were in.
Something I have also realised is how many actors and actresses that seemed to be huge were only ever really in a handful of films or active over a fairly short space of time, for example Ginger Rogers and Fred Astair were only ever together in something like 10 films including the first one they were paired in where they were only in it for about 5 minutes, but they became so iconic it felt like they were in loads.
I really need to watch amongst others:
It's a Wonderful Life
The Godfather Part 3
A Clockwork Orange (I've had that as part of a Blu-ray set for years, never managed to sit down to it)
One Flew over the Cuckoos nest
Various of the old Hepburn/Monroe/Jack Lemmon/Bogart films/Sophia Loren (picked up a BD set of some of her films cheap recently).
The hundred or so films I've somehow managed to buy but not get round to...
On a general note, for some of the classic/older films the BFI player can be a bit of a gold mine, as they've got a bunch of stuff that doesn't seem to be on Prime or Netflix and they have it listed so you can see their catalogue before you sub, and they do them in collections with a number having an introduction. The downside is that it's a browser based player and it feels quite basic
Lots of classics I’ve not seen, one that sticks out is Casablanca
I finally got round to watching that the other week, I'd had it on the tivo for about a year.
It was good, quite a different feel to it compared to anything modern, and a twist I somehow had managed to avoid seeing coming/spoilers of.
TV:
Game of Thrones - I was never sure on this, everyone I know raved about the series at the time!
The Wire - Heard good things and next on the list.
The Sopranos - Started but didn't grab, might need to revisit.
Twin Peaks - Going back a few years but this series always intrigued me.
Film:
The original Hollywood blockbuster horrors starring Boris Karloff / Bela Lugosi! Frankenstein, Dracula, The Mummy, Wolfman - always put off as I'm too chicken
The Wire is excellent if you haven't seen it yet, as is Twin Peaks (in a weird way) make sure you watch the third season and IIRC film.
The hollywood classic horrors are great, very much a thing of their time in the limitations but you can see exactly how so many later films not just copied the basic story but the structure and they're not really scary, if anything they're really tame by modern standards. IIRC the "Universal classic monsters" set has the original standalone Universal monster movies and is quite cheap (about £20 for the 8 films, with a host of extras including the Spanish version of Dracula which was filmed on the same sets at the same time).
*I keep a load in my "for later" and "wish list" baskets on various sites and typically have a rough idea at what point they get bought if I've got the spare cash.