What's a less expensive way to change old tile in kitchen?

Peel and stick tile decals are a simple and eye-catching option. They come in a variety of patterns, from modern to traditional, like this one: http://a.co/bNxYVgw

For an even less expensive option, you can also paint tile. You can do a solid color, or with a little more time investment, you can use a stencil, like this Hometalker who painted her bathroom tile in a striking black and white pattern: http://www.hometalk.com/diy/paint/i-painted-and-stenciled-my-ceramic-tile-30107044 It looks beautiful!

Here is an article that might be helpful - http://www.hgtv.com/design/rooms/kitchens/inexpensive-backsplash-ideas - good luck

Unfortunately there is no cheaper way that the correct way of changing old tile:

Everything- tile, backing, glue, screws, and anything else that you may find underneath the tile must first be removed before any new flooring installation.

There are lots of other posts here on Hometalk about the work involved in removing tiles.

Paint it!! that's just what I am in the process of doing.

Cover it up with vinyl plank flooring. You can get it in lots of patterns...either tile or wood patterns. Just lay it out over the tile, use a utility knife to cut it. It is completely waterprooof and fairly inexpensive as well.

If you try to put any kind of flooring over existing tiles, immediately the height of the floor will be raised. The areas presenting the most problem will be the transition areas, such as doorways and entrances. These transition areas will be very hard to integrate, to keep clean, and to finish safely and securely so that they do not become a tripping hazard.