Hey duders. I've stumbled upon a few things that I have no idea what they are, and have had no luck figuring them out. I thought it would be a good idea to start a thread where we could attempt to figure some of these things out and compile them. Feel free to ask about certain things you've found but can't figure out or post known secrets. It would be appreciated if we could keep spoilers to a minimum, but this thread will most likely contain spoilers, so read at your own risk. Happy Spelunking!
Chip Music - Rarely, a special chiptune music track will play which is unique to the area you are in. This has no change on the level. (Confirmed by designer Derek Yu here)
City of Gold - Items needed: Udjat Eye, Ankh, Hedjet, Scepter. Directions: Obtain the Udjat Eye (Mines Chest), and the Ankh from the Black Market ($50,000/steal). Find the Moai statue in the Ice Caves and commit suicide near it. The Ankh will revive you inside of the statue, and will grant you the Hedjet. Next, in the temple stage, go to Anubis and kill him to gain the Scepter. Once you have done this, a golden door will appear leading you to the City of Gold in one of the first two Temple stages. The Book of the Dead is obtainable here; it will allow you to complete the game the 'hard way'.(Courtesy of IH8PITT)
Complete the Hard Way (To Hell and Back) - Receive the Book of the Dead from the City of Gold [directions to the CoG above]. Take this book to the final boss fight. It will lead you to a secret door that floats above the lava. It is necessary to use Olmec's head as a platform to reach the door. This door will lead you to the secret Hell area. Tip: If possible, kill Anubis II. Otherwise, he will follow you between levels attempting to murder you. (Courtesy of isbecome)
Crysknife - A secret weapon in the Worm level which lies at the bottom of a stomach acid pool; it replaces your whip. (Courtesy of Peanut)
Damsel Sacrifices - Place a damsel on a sacrificial table and receive an item. The item received depends on the amount of 'Favor' for the person sacrificed. Living damsels give more than dead damsels and favor adds up during one session. Here is a list of favor values/gifts. (Courtesy of YoungFrey)
Ghost Run - If you lead the ghost over gems, they will turn into diamonds. (Courtesy of MikeGosot)
Golden Idol Sacrifices - Place a golden idol on a sacrificial table and receive a Golden Monkey who generates gold.
Haunted House Level - In the Jungle during "The Dead are Restless" if you bomb the tombstone with the crown, and then bomb again directly underneath it, you are led to a secret level. There is a character inside the top of the tower. The easiest way to reach him is to use a rope and get on top of the tower and bomb your way in. (Courtesy of joshthebear, bushpusherr)
Main Menu Spears - Sometimes special objects will hang on the end of the spears that appear as you select a mode. Items like the Ankh, Olmec's face, and an alien have been seen. These changes seem to be solely cosmetic.
Mothership Level - During the 'It feels like the Fourth of July' event, at the very top of the long tower that spawns is an entrance to this level. There is an Alien Queen in this level, and a rocket launcher will be dropped when killed. (Additional details from IH8PITT)
Super Meat Boy Character - Unlocked in the Worm level. He appears trapped inside of a bubble. (Courtesy of Peanut)
Udjat Eye - Obtained in the mines by using the gold key to unlock the chest. When it glows and beeps, it is alerting you to the secret entrance of the Black Market. You might have to blow up some land in order to find the door. (Courtesy of slayergnome)
Worm Level - In the Jungle or Ice Caves, throw a damsel on one of those red sticky ball things and jump on it with her. A worm will will emerge and eat you, sending you to a level inside its stomach. (Courtesy of Peanut)
'Level Feeling' item secrets:
I hear snakes, I hate snakes - A pickaxe is always buried at the bottom of the snake pit. (Courtesy of IH8PITT)
The Dead are restless - If you bomb the tombstone labeled 'ASH' there will be a shotgun buried underneath it. (Courtesy of IH8PITT)
I smell wet fur - Killing the Yeti King rewards you with Spike and/or Spring Shoes, Ropes and a Compass. (Courtesy of IH8PITT)
I sense a psychic presence - A jetpack is hidden in the wall behind the alien lord. (Courtesy of IH8PITT)
Edit: Wow, these are some pretty interesting secrets. I'll add them to the lists (providing credit, of course) up here for convenience.
Edit 2: Keep these secrets coming! I also deleted my 'Weird Happenings' section because I figured out those things were only cosmetic changes.