Is it safe to remove an FC cart while the power is on?

[boye]

I accidentally removed my copy of Super Mario USA using the eject lever while the power was on Would this damage my FC?

[FAMICOM_87]

No. Don't worry. You can even put the   while the console is On and then reset to play the game. When I was a child I use this method often  

[boye]

So, it's ok to remove the game with the eject lever, right?

[Jedi Master Baiter]

Just don't do this with a battery-backed game.

[P]

Nintendo recommends against it but damage is rare, especially if the ground pins are longer than other pins so that they are disconnected last. For many reasons though It is possible that it may cause strain on the Famicom and cartridge, so I wouldn't do it too often.

Some people hot swap a flash cartridge with a program that runs in RAM with a cartridge with some special hardware they want to test.

Back in the day there was a famous glitch by using the hot swap method to access 256 different worlds in SMB. Worlds past world 8 would load non-level data as level data, causing all kinds of impossible levels with things like swimming in the air and floating marine enemies on non-water levels. This is what inspired many things in SMB2j (like mid-air floating bloober/gesso and the fantasy world).
Tennis can be used for this, but Family BASIC allows you to choose world more accurately.

[jpx72]

I killed a few glob-top pirates by hot-plugging them.