Dammit- I think it's my fault that goldeneye got brought up in this one. Shoulda kept my mouth shut at the mana bar I guess...
Oh well, seeing as I'm here, may as well explain WHY goldeneye holds up.
Non-Linear Levels- pretty rare back then, just as rare now. The levels were often built like actual believable layouts, like Thief was, so exploration was rewarding and there were different ways to do everything.
Rambo style sometimes WILL get you massacred- Forgetting for a moment that it was the first to do stealth in a console FPS, it also did it damn well. Even today if you get lazy you will be overwhelmed. You can still barge through guns blazing in some levels, but there's nothing quite like breaking out of a cell, unarmed, finding some throwing knives, and then taking down absolutely everyone in an underground bunker through patience, timing and skill blah blah blah... these days everything's just a mindless corridor.
The best difficulty setup ever done- There was actually a point and incentive to play on all difficulties. Higher difficulties had more objectives, and sometimes new areas. Each difficulty level unlocked a bonus level of its own when they were all finished too. Modern games STILL mostly don't understand that with a higher challenge there needs to be bigger rewards.
offline Splitscreen with four players- We don't care what limitations you have with a console's hardware, if goldeneye could do it with the 64's measly hardware, you can do it today. I'd go further and say any shooter that doesn't have multiplayer bots like Perfect Dark brought is a step backwards, too. What the hell, Killzone 3? what were you thinking, COD: WAW?
massive arsenal of guns that had real weight to them- I'm not saying all modern games do this but a lot of games make the guns a bit lacking in punch. Even tiny pistols in Goldeneye slide back and bark loudly as the shell pops out in front of a decent muzzle flash as you aimed exactly where you wanted to shoot with your own targeting, not some PC style crosshair trying to work on a controller. And there were more than thirty weapons! and you could carry them all at the same time! Why did you do this to us, Halo? And what the hell, DNF?
No handholding- You got your brief, heard you're objectives, and were thrown in to work it out for yourself. One thing that drove me insane in nearly every Bond game since is the fact that when Bond is out doing a mission, the entire staff of MI6 is listening and offering so called 'advice' all the time, like saying "That vent, 007!!!" as I am facing a very obvious large vent that is filling my screen. A lot of modern games guilty of this one especially.
cheats- Do I really have to explain this one? It's simple- complete a certain mission, on a certain difficulty, in a certain time, and you get a fun reward. Playing with cheats will not unlock the next level/bonus/whatever. It's simple, it's foolproof. It's fun. Thank god Timesplitters continued much of this legacy.
Bottom line is -and I can't believe I have to tell you this Yahtzee- good games aren't just about graphics. Sure the 64 is old and had simpler games in its time, but that just allowed devs to get more done right (in principle, anyway. Nobody forgets Superman 64). There are many 'best game of X console' discussions out there, but it's the N64 that gets the most debate about which of it's games where the best game of all time.
Tell you what though, you were right about the fish offering in OOT. Took me weeks to figure that stupid logic out. And I had never played a zelda game before last year either.
Sadly enough all the good Nintendo games that weren't first party are on other consoles now. That includes the Goldeneye reboot. 
