In level 1 ("Seppuku Station") is a TV playing footage of Michael Faye's Singapore caning incident. After you get the gold key located on the crates, you'll notice a window of a room above which houses an Uzi. If you stand along the ledge with this room to your left, you can make out another window dead ahead. Make a running jump towards that window and you'll land on the ledge of that window. Inside, you'll see the video along with some weapons and a medkit.
In level 4 ("Dark Woods of the Serpent"), once inside Ripper Valley, go downstream from the waterfall. You can dive under where the river runs under the rock ledge. When you emerge from the water the game will say that you found a secret area, but there is more in this area you should investigate. Head south and jump on the short wall and you'll see an "unordinary" rabbit, a chalice and a knights helmet. This is a reference to Monty Python and the Holy Grail. If you blow up the wall beyond the chalice, you'll be rewarded with two fortune cookies and some missiles as well.
In level 4 ("Dark Woods of the Serpent"), near the end of the level you will see a flying carpet, jump to it. It will start flying down a lava pit. You will see two caverns to your right with a ninja firing at you. Kill him and jump to the caverns. Behind the caverns you will find a corridor with some explosive barrels. Shoot them (from a safe distance). You will now see, through a break in the wall, a hidden room with someone at the opposite end. Get closer and you will see that it's Lara Croft (from "Tomb Raider") imprisoned.
In level 20 ("Stone Rain"), the last level of the game, just as you enter the grated area towards Zilla's lair, you can see a nuclear missile under the grates. Push on the wall the the left side and it will open up and you can reach the nuclear missile. You can also run to the right and it will lead into a huge area under the volcano that has lots of items and the dead Teenage Mutant Ninja Turtles.