I have a 3inch space between the back of my stove and wall.

They make these things called gap guards. Here is a link to what they look like - https://www.amazon.com/Stovetop-Extender-SE23WHI-Oven-Guard/dp/B00290VZ2G - maybe this would be helpful

You don't say what type of stove you have. Some brands have accessory filler strips you can install, like this GE rear filler strip: https://www.amazon.com/GE-WB07T10680-Range-Filler-Strip/dp/B00D8L9CWK

You could put a wood 2x4 just below the top of the stove. Then if something does fall behind it you can at least pick it up off of the 2x4. Adding a spice shelf above it for decoration might be nice, and help hide the gap.

How about a metal shelf that would be even with the stove? Should help a bit. I bought metal picture rails from Ikea for my daughter and put plates over her stove. http://www.ikea.com/us/en/catalog/products/60310617/

I don't know if it would be deep enough, but might help block some things.

If you have head room, have a shelf put there

How about a narrow shelf, the length of the stove? Have it set close to the top of the range.

Bed Bath And Beyond has metal baskets that are oblong that you could put up so they are close to the level of the back of your stove. I would watch what you are putting in them as they may get affected by the heat of the stove. I have mine on the stove control upper part, mine isn't like yours that is flat across to the back. Didn't want controls accessible to little grandkids. I keep things like spices I use the most on meat that doesn't have high sugar content and garlic powder.

A narrow shelf would be great. You could put some cute salt and pepper shakers on it.

First I must ask, Why is it not pushed back to the wall??? It might be so that heat can not start a fire in the wall behind it! So, I'd find out somehow. then maybe something like rabbit wire or even chicken wire folded to fit the space would still let the heat out, but stop things from falling behind it. The wire could be nailed or stapled to the wall, but is stiff enough to hold its shape by not fastening it on the stove side. But this space might not supposed to be blocked completely....

Fill it with a chain of flowers. You can get them at Hobby Lobby. Dollar Tree they are plastic and cloth so they never need water and when they do get dirty you can handwash them. Also you can change them for the Holidays to make your room more festive. Good luck.