I'm confused -- the picture shows a colorful backsplash. If that is your dream and not your reality, here are my ideas:

Buy a sheet of plexiglass to screw in over your stove, the same size as the total space. You can put it up with four screws; easy to spackle and repair if you need to move. Put behind it a sheet of beautiful wrapping paper, wallpaper or anything else you like.

If you are not too messy in the kitchen, removable wallpaper or vinyl decals could work. No holes in the wall, but if your spaghetti sauce splatters it could be time for new decals!

Hang colorful plates on the wall in the backsplash area. One small tack hole per plate.

You can try self stick tiles. Just did this myself and opted to use them stuck to the wall behind the sink. But behind the stove (high heat, don't know if the stick would hang in there) I placed them in a photo frame (no glass) which hangs on the wall instead. Look up "smart tiles" on Home Depot for somthing a bit more pricey. What I opted for were vinyl "self stick tiles" from Lowe's which I bought by the piece. Happy with the results and easy to clean, and affordable.

I used this great tin panel supplier when I remodeled my kitchen. You can get real metal panels (not those cheap plastic ones you find at the hardware store) for about $9 for 4 square feet. Awesome! And fire safe! http://www.thetinman.com/

you could staple oilcloth to the back splash area. it cleans up nicely.

I love that backsplash! You could do so many things in regards to accessories to make the colors pop against the white. If this is your backsplash now I would just play with the colors in it. There are so many to choose from.

You can buy wall panels from Ikea called FASTBO in which you could tape on top of the existing backsplash.

@TiffanySeattle - do you have a pic of your kitchen with the tin backsplas? Would love to see how it turned out. I'm wondering if I use this to cover ugly tile backsplash in my kitchen - without having to rip it out. Thoughts?

You could put whatever you fancy on a piece of masonite or thin plywood cut to size and then just fasten it on in a few places with screws or velcro or really strong double sided tape.

I was a renter with an ugly kitchen that had no backsplash, so I painted some Inhabit Wall Flats a glossy white and used 3M command adhesive velcro strips to hold them on the wall. I also ran some Ikea Dioder light strips under the cabinets and hid the wires. It looked really nice and doubled as mood lighting.

@TiffanySeattle--thanks for that link. I second that I would love to see any pictures you may have of how you used these in your kitchen remodel.

I know my answer is not what you are looking for but I would keep it!

I am confused...do you already have this back splash?

I too was contemplating this recently. This is probably the BEST short term and removable option I can up with -- http://pinterest.com/pin/123637952240315468/

Use plastic place mats of your choosing (could even find at the dollar store) and use a strong but easily removable adhesive (like the 3M command strips that you just pull and stretch to release).

Like Mel_Bell said, you can use placemats. I got some cute ones for cheap at Ikea to liven up my plain, off-white renter's kitchen.

My vote is for the tin backsplash, but the placemat idea is good, too. If you live in a part of the world without an IKEA (le gasp), Dollar Tree carries some very cute ones.

I would not use the sticky tiles that someone else suggested - over the stove. I believe the heat will melt the adhesive, very slowly and unexpectedly you'll have a vinyl tile fall on your stove when you're not looking... and could be dangerous.

I like the plexi or glass with wallpaper or something behind it.

I hate to say this ... but ... if you want to paint it... paint it. If its an improvement your landlord probably wont care (you could always show them the color ahead of time and just ask). Or if you do it... and If they dont like it when you move out... you can just as easily paint it back to white.... they couldnt rightfully charge you for anything if you resolve it.

I also found this question confusing. Also what does "senior on a fixed income" mean?

I am moving in to an apartment tomorrow and the kitchen has grotesque MIRROR backsplash. Aside from being ludicrous (who wants to see their own face while cooking?), it's going to be a nightmare to clean too. Can someone please tell me what to do?

@Drops of Jupiter: In the U.S. senior citizens (age 65+) receive a modest retirement income (based on taxes paid during their lifetime) from the social security administration. It's intended to supplement a pension, but since the economic crash, many older people rely on this income alone.

For areas OTHER THAN the kitchen, you might try a trick I've read about but never tried. Supposedly it is possible to dip fabric in old-fashioned starch and then smooth it to the walls like wallpaper; then it just peels off when you need to remove it. You might try Googling that.

The placemat idea is genius!

Dunno if this is possible for you, but to dress up the backsplash of my kitchen I put some postcard prints (of art nouveaux cooking drawings) in little cheap 3x5 frames and hung them up along the back splash. Nothing like a framed picture to look classy and make the kitchen feel more like a "room"! They've had a few spaghetti sauce splatters over the years, but I just wipe them down once in a while. They're cheap, so if anything truly terrible happened to them I could just toss them in the garbage and move on.