Can't fully complete the civil war questline, you can do up to Balgruff.
Can't do Dragonborn's Main Quest, you lose access to the Skaal and a couple of other dungeons although you can still access the island. There's also a Dwenmer ruin quest that can still be done without the main quest, you just have to go to an extra Dwenmer ruin.
You can't do the quest that involves the Alkir, that quest only unlocks after Bleak Falls Barrow.
You can't do Mephala's quest, that unlocks after you kill your 1st dragon.
You can't collect all the Stones of Barenziah because one of them is in the Thalmor Embassay.
You can't get the House in Whiterun, you also can't become Thane Of Whiterun or Thane Of Windhelm without going to Bleak Falls Barrow.
I think that's all the major stuff unless I'm forgetting anything. It's definitely a design philosophy that I despise.