What changed over the years?
The culture of being hard on the players
Something that would hit anyone who played AD&D 1st edition and was left in the dark for 30 years is the effort put into empowering the players. Depending when you land (let's take the latest 2 editions), the force of impact will vary. Originally you'd roll for your stats, put the numbers in order and hope you'd fill the requirements for your class. You wanted to play a fighter. Sure you can. But because you roll your stats in order you could end up with a lot of intelligence and no strength. Oh you'll make a Wizard instead? Roll for your hit points and if you get 1, well too bad buddy. You can be killed by a kid throwing a rock at you. The idea of balance in the early editions was almost absent. A wizard would be almost useless at first level but if you manage to survive the crazy adventures you'll be the most powerful character at the table. 30 years later, dying is still a possibility for the Wizard but depending on the edition you play, it'll be much harder than before. Wizards never run out of options in combat. They may run out of their really good spell but they still have access to offensive at-will spells and they don't have to fight with a stick.
Originally the Dungeon Master's Guide entitled you to supreme deity of your own world. Today the language is toned down a bit and the Dungeon Master's role is mostly the same but they don't push you on the power-trip as much as they used to. The iconic deathtrap/killer dungeons (Temple of elemental evil, Tomb of Horror etc.) come from that time where torturing players for fun was part of the hobby. I'm might be exaggerating a bit, but so was Gary Gygax.
Diversity is an understatement
When mxyzplk says the game got fatter, it's not a lie. Here's a list (from the top of my head) of the races available since the beginning in the core books: Dwarf, Elf, Halfling, Human. A little bit later the Gnome, Half-Orc and Half-elf showed up but the list was minimal. 30 years later, the list is big. 30 years later you can play a Dragonborn (basically a humanoid dragon) and an Eladrin (a type of elf who can teleport). This should definitely be a surprise for any old school player who suddenly looks at the new material. Want to play a walking robot made out of metal and living material brought to life by magic? That's a Warforged. The game options exploded. If you include Pathfinder, you have a class entirely focused on firearms (Gunslinger). Point is, compare the number of options available in the Player's Handbook of 5th edition with AD&D 1st or 2nd edition.
What didn't change
Dungeons, Dragons, saving throws, crazy adventures with your friends. That part of the game didn't change much over the years. Some editions might smell more like D&D than others, but what's great is that most of them are entirely available today. It's easier for me to grab the 3 core books of AD&D 2nd edition today than it is to get my hands on many recent new games at my game store.
So for me, when I hear "the game didn't change much", it's a little bit misleading. From it's inception to today, the game changed a lot. But you'd recognize it at the 30 years later reunion party. It'll have a few kids (tons of retro clones, board games and derived products) but D&D is still D&D.