I've known people who use old pieces of carpet for paths. After its been there a while it looks just like dirt. :)
You could also lay cardboard down and replace it as it decomposes, or replace it with bricks or stones as you find and gather them.
Totally agree with Melvalena and the scraps are usually free from carpet installers. Another idea is used or spare shingles or roofing material. Some might comment on the potential for bleeding of nasties but I've used it before with no issues. An el-cheapo bale of hay or staw goes a long way too. Cheers!
I like the cardboard ideal. I can toss it into the compost bin when it gets broken down. I can get an endless supply of cardboard. We are also getting some gravel for our back drive. Maybe I will sneak some out of the pile when its delivered and make paths. When my husband ask about it I will just say oh that has always been there. He won't buy it but it's worth a shot. :-)
I agree with Melvalena as old carpet is just fine, and does it wear! It cuts down on weeds and lets an even a disabled person walk without stumbling.
This is a great idea having several different kinds of paths in the yard, I like this one the best. I use my carpet on a raised bed and have slipped while going up hill, but with the carpet down, I don't slip when my veggies are large I can still manage the carpet better then the concrete blocks I had down.
Building a gravel or crushed stone path is both inexpensive and lovely and adds "crunch to the garden." There are articles all over the web about how to do that and a great book "Garden Path" by Gordon Hayward which describes all kinds of paths and how to correctly build them.
Dig a little 6" - 8", lay 1" - 2" of 3/4" gravel, then put down landscape fabric, and 4" of screened gravel, then 1/2" of fine gravel. Tamping in between layers.
It's not as easy as carpet but I think it looks nicer and will last longer. Some people just dump the gravel and start walking on it.
LOL! Good luck, it's worth a try!
No, I have a berber carpet which is a tight short loop and don't have a water problem infact I left it out this past winter in the same area I never stored it away.