Super Mario 64 has quite a lot of coins to collect! There are 2092 coins scattered around levels, plus another 580 in bonus stages, for a total of 2672 coins. Of course there's also coins from Bowser during boss fights but we don't count that. If you were to go through every level searching high and low for every single last coin, you'd probably come up a couple short. There are two coins in Super Mario 64 that are completely hidden from view.
The Secret Coin
There's one coin on Snowman's Land that's placed just out of bounds. To see this coin you need to go to the thin little wooden path on the giant snowman. This coin is out of sight, so you're going to need to tilt the camera in a way that allows you to see it through the wall. If you stand in the correct spot, and tilt the camera down, you'll be able to view it. This coin may be hidden, but you can still collect it. There's a cannon that's next to the spot you start at in this level. Hop in, and then line yourself up with screenshot #3. If you hit the wall in the right spot, you'll have acquired The Secret Coin!
The Unreachable Coin
For this one you'll need to go to Tiny-Huge Island, on the Huge side. The developers likely made a major change to this level and forgot to adjust the height of several coins. Right next to the hole that shoots those cannon balls, are 3 coins. The developers placed these 3 coins on a slope, but they placed them horizontally, instead of diagonally with the slope. The first coin can be seen, and collected normally. The second coin cannot be seen normally, but it's still close enough to the ground to be collected. And then there's one more. This last coin is the only coin in Super Mario 64 that cannot be collected legitimately. We can see this coin by dropping below, and tilting the camera against a wall like we did earlier. You can watch that coin spin all you want, cause you'll never get it!
Unreachable Coin Update
After being taunted by the unreachable coin for many years someone has managed to collect it. Unfortunately it involves such precision that I highly doubt it can be collected normally on console. Collecting it will instead need to be done in emulator with both save states and slow down. First you need to go to the top of the mountain and ground pound it to lower the water. Then one needs to make a very specific jump towards the seam of the mountain. If done properly you will clip through and land inside the mountain where the water is. Once inside the mountain, swim a bit lower and face the unreachable coin. Then head towards it. Between the edge of the water and the void there is a single frame where Mario can make a jump. Make a jump towards the coin followed by a kick. If done properly you'll just barely collect the coin and land back in bounds.
I think we can still safely say the unreachable coin will remain unreachable for most gamers. Thanks very much to Valerie for letting me know about the unreachable coin being collected. To view footage of someone collecting it please check out this video.
Written by Kevin Ames
September 9 2012
Updated August 21 2014