A really simple question, but I was wondering how come some games stay in RAM even after resetting,
and how could I put something in RAM which stays there after I reset the computer?

Maybe becouse of the cmos/or other kind battery

Ram is not erased after a reset. There reason why some games restart after a reset is because they used to be in ROM. They have an indentification code 'AB' on adress #4000. The bios searches for this code in all slots and if it finds one it boots it. With the msx2+ bios this problem is fixed. When a hardware reset is done the first byte is overwritten (and if it is in ram the byte 'A' is lost). When a 2+ gets a software reset this is not done and the rom in ram will still boot after rest.

Depending on the DRAM chips used it can take (quite) some time to have it 'forget' its contents after a while. When the ROM ID "AB" is detected on address $0000, $4000 or $8000 (unlikely as the ROM writes $00 to $8000 - $8002 to do a BASIC init) it will read the next two addresses to start the program (which is usually a game).

When you're lucky, a hardware reset will either make the DRAM instantly forget or have it changed a bit... This way the ROM ID "AB" is gone and the game will not start anymore. As msd already stated the soft reset will not change the DRAM contents at all.

It's kind of fixed in the MSX2+ and MSXturboR because that first address of each block/segment is used to dertemine the mapper size which is printed in the logo screen.

I remember I used to rip graphics from games this way, by rebooting when the image was up and then loading AGE and somehow (I forgot how) pasting it in there.

That's a video memory issue. Video RAM isn't erased upon a reset, only the part necessary for the boot sequence (and entering BASIC or whatever), is overwritten. Most of the time you'll have the graphics on the lower 64kB VRAM at your disposal, and most of the time that's the place where many games put there game tiles in. For example this way it's possible to rip graphics from Pumpkin Adventure III (I used to do that, a couple of years ago )

I remember being at a friend with an NMS8220. I loaded my copy of Zanac there from tape.
Even after about 2 minutes, there were traces left of that game in RAM!