Bandanas are available at craft super stores, discount stores, and even "dollar" stores. Some of them are 100% cotton and some are not. If the package label doesn't specify the fiber contents of the fabric, look for the label that is stitched into the hem of each bandana. Look closely at the fabric to see if it is firmly woven or loosely woven. If it firmly woven and all cotton the fabric from bandanas should work well in your quilting projects.
I recently purchased 100% cotton bandanas in a packet of two for one dollar. Each bandana is twenty-two inches square. If my math is correct one 22" square bandana is at least twenty percent more fabric than a fat quarter. Can you imagine buying a fat quarter at the quilt store for fifty cents?
Bandanas come in many patterns and colors. I have purchased tie-dye, batik, floral printed, embossed, glittered, solid color, and licensed character print bandanas. All are a wonderful resource of unusual fabrics not always available to the quilter in traditional stores.
Be sure to check for fiber content on the bandanas if that is important to you. If you don't mind using some fabrics with polyester there is usually a wider selection.
Neckties have been used for quilt making for many years. The easiest way to obtain neckties is to let men know that you are collecting old, stained, damaged, and out of style neckties. If you tell several people you are collecting neckties they will bring you bags of them. Most businessmen have several ties hanging in their closet that need to be discarded and when they know they will be recycled in a quilt, they are willing to sort them and share with a quilter. Old neckties can also be purchased at thrift stores and yard sales.
First wash the neckties to remove spots and stains. Most neckties are silk or polyester. You may launder them by hand or place them in a mesh bag and wash on a gentle cycle in your washing machine. They might shrink but that is ok as you are cutting them into smaller pieces anyway. Neckties should be line dried or dried flat. After the neckties are dry, rip out the stitching and remove and discard the interfacing. Press the necktie fabric from the wrong side using a cool iron.
There are quilting instruction books available featuring necktie quilts. There are also patterns scattered in magazines and general quilting books. Many patterns available using neckties are simply pieced quilts using the necktie fabric but the piecing has no relation to neckties. An obvious necktie pattern would be the traditional "bow-tie" block. There is a pattern for a pieced shirt block using the tie fabric in the tie position of the block. A crazy quilt would be an unusual option. Another option is to simply stitch the ties together into a flat circle and appliqué them to a larger background fabric. Quilters in the past have made many creative quilts using old neckties.
The obvious place to purchase fabric in the thrift stores is in the clothing department. Sometimes a beautiful blouse or dress will have a substantial amount of usable fabric. A large men's shirt will provide plaids, checks, and stripes. There will be large pieces of fabric in the back and front of a blouse or shirt. You might need to cut away some areas such as collars, and cuffs, but if your quilt patches are small enough even the sleeves could be used. If you find a dress or a full skirt there will be lots of fabric to incorporate into your quilting projects.
When using fabric from clothing, be sure that the worn places are cut away and the fabric is washed to remove any soil or stains. If you do find a stain or two you can simply cut it off and discard. Much of the best fabric can be found on the "bargain" table where the damaged or stained clothing is sold.
Our grandmother's made quilts from recycled fabric as that was all they had available for their utility quilts. Remember to check for fiber content. If you prefer 100% cotton you would need to select from clothing that is all cotton.
Another find at thrift stores is cloth tablecloths and napkins. Tablecloths come in many sizes, colors, and shapes. A large size plaid or checked tablecloth would be very nice in a "country" style quilt. A large damask or linen tablecloth could be used as a background for appliqué for an elegant quilt.
If you appliqué small items you might want to purchase cloth napkins. There are cotton cloth napkins available but most prevalent in the thrift stores are linen or damask. Damask has shiny and dull areas woven into the fabric. Applique a floral arrangement in the center of a damask napkin and you have a wonderful pillow, center of a wall quilt, or blocks for a larger quilt.
Other thrift store items
Don't forget all the other fun textile memorabilia available at thrift stores. White or ecru doilies could be hand stitched to colored background blocks and make a very beautiful quilt. Doilies can be cut and used as partial blocks. Remember to put them on a contrasting background so they show their intricate stitches.
Hankies could be stitched to background blocks as a whole or cut and used as portions of pieced blocks. Embroidered pieces might work as partial or whole blocks stitched together with or without sashing. Old fashioned ladies gloves would make wonderful embellishments for a vintage quilt.
Yard, garage, and church sales
Don't forget inexpensive fabric available at yard sales. Last summer a quilting friend phoned me to share her good news. She had purchased a large lot of unused fabric yardage at a yard sale for a very small price. The majority of the fabric was quilting cottons. There were so many large garbage bags full of fabric she needed to make two trips to get it all home in her small car. She went through all the bags and kept all the fabric cuts that were in colors and prints that she liked. Then I looked through the bags and chose the fabric colors and prints that I could use. I took one large wastebasket size bag home and washed my new stash. When it was all clean and folded I counted 40 yards of fabric. My friend had seven large bags leftover to donate to a church charity. I have no idea how many yards she kept for her personal stash.
Our local quilt guild schedules a yard sale for our monthly meeting on alternate years. Each member is welcome to bring her cuts of fabric, books, patterns, and other quilting related items and sell them at the meeting. These meetings are well attended and some great fabric bargains are available. One quilter was selling unused fabric cuts for one dollar each. All the pieces were at least one yard and up to two yards.
There are many places a quilter can find good fabric deals for stash builders. Many times when people learn that you are a quilter they immediately think of that bag of fabric they have in the back of their closet. Graciously accept any and all fabric that is offered to you. You might be surprised at the good things you will receive. You could get a selection of vintage feed sacks, that fabric you had five years ago that is all gone and out of print, or just the right color print for your latest project. And if you do happen to be given some bad stuff you can always drop it in the nearest dumpster.
You forgot to mention auctions -- I attend auctions all the time especially household auctions, if the ad mentions crafts or sewing related items or quilts, you can usually count on fabric of some sort being there as well. I have bought 3 or 4 boxes of fabric this way and they are always just what I seem to be looking for.
I know of another source for inexpensive/free fabric. Try your local "freecycle" to get scraps/yardage from those that have purchased fabric but are not interested in using it any longer. I have received many bags full this way and I use the scraps to make charity quilts!!!