There are a few things that some Super NES games check before booting up. If any of these checks fail, some sort of error message is displayed on screen. All of these checks had to be done via software, so not every game has every kind of check. Let's go through a few of the more common ones.
Mario's Super Picross probably has the fanciest error screen I've seen.The most classic error message is the region-lock message. While the North American Super NES had different shaped cartridges to prevent players from inserting Japanese or PAL games into the system, the Super Famicom and PAL SNES had identically shaped cartridges. Also, it wasn't too difficult to modify the plastic shell of the North American Super NES to accept PAL cartridges anyway. However, lots of games checked for region compatibility via software.

Each Super NES game has an internal header that denotes what region the game is meant for. And each SNES CPU has an internal register that identifies it as an NTSC or PAL model. Therefore, it was easy to check for compatibility. If the game notices that they don't match up, an error was often thrown up on the screen.

An odd error message that comes up in a smaller subset of games is the controller error. Nintendo made it clear in its game design documents that games should ensure the correct controllers or other input devices are plugged in. If the wrong kind of controller is detected, and error should be displayed. For example, some games will not start if a Super Scope, multitap, or SNES Mouse is plugged in. You have to unplug the offending controller and restart the game.
I like this screen because it's so kind. Also the kerning is completely different from the other message for some reason.
Though, there's nothing stopping you from just plugging in the controller again after the check is done, usually right at bootup.
The text color actually cycles through all 32768 colors. The cycling is done by just incrementing the color value by 1 each frame.
The last error message--the most interesting--is the piracy check. The easiest kind of piracy to check for back in the day was game copiers. They would essentially allow you to copy the ROM of a real game cartridge into the storage of another device, which would present itself as ROM when inserted into the console on its own.
Super NES games could use a variable amount of ROM and RAM in their cartridges. In order to maximize compatibility with games, copiers usually had room for the largest games in both the ROM storage and RAM departments. However, having an amount of memory different than intended could be detected via software. So many games used this trick to identify piracy, and display a scary message about copyright infringement.
Yoshi's Safari here is a game that doesn't have any on board RAM at all. The trick it uses is to copy the internal ROM name of the game, "YOSHI'S SAFARI ", to address $700000 (and other various address around here). Then it reads that exact string back. If there's a match, that means that there must exist some sort of RAM there. It actually does six checks in six different locations, and if just a single one matches, then the error is displayed and the game locks up.
From Yoshi's Safari. Pulling out the US Code section numbers now, how scary! Also again with the completely different font from the other message in this game.
Some games do have some RAM on board in order to store the game's save data. I showed Mario's Super Picross above, but Earthbound is also a good example. First, the game stores the constant #$30 to address $307FF0. This indeed writes this value to the cartridge RAM. Then, #$31 is written to $317FF0. Notice that this is the same address as before, but the bank has changed. Earthbound only has 8 kilobytes of RAM on-board. This second address is past the 8-kilobyte limit. Due to how the cartridge RAM is mapped to the address space, it gets mirrored multiple times. So even though the address is different, this effectively writes to the same location in RAM. This should overwrite that first #$30 with a #$31. However, since a copier would be likely to have more than 8 kilobytes of RAM, these two addresses would actually refer to two different locations. So there is still a #$30 at $307FF0 and a new #$31 at $317FF0. All the game has to do now is check if $307FF0 is #$30 or #$31. If it detects the former, then it knows a copier or some other sort of device other than an original game cartridge is present, and shows the error screen.
I imagine if these screen appears, the FBI busts through your doors screaming "We have a 2319!!"
Earthbound has a lot of other piracy checks too, but maybe we'll look at those another time!
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