I recently researched alternatives to glass for permanent framing/protection, and I found that glassine paper is supposedly a good cheap alternative. I ordered it on Amazon, but I was very unhappy with it. It was barely transparent and the glassine obstructed the viewer from seeing my art and appreciating the colors and the beauty, it was like looking through a smokey window. So now I'm looking for any other suggestions for paper that would protect my art and have a generous amount of transparency.
Soft pastel is literally the most difficult "painterly" media to protect. Generally speaking, the appropriate way to protect pastels is with a so-called shadow box, where the paper or board is floated above the backing plate of the frame and still has air-space to the glass. (See my drawing below.)
This is a pretty material-intensive method, but it serves to isolate the pastel from touching anything, including the glass. You have probably noticed that applying fixative to soft-pastels will change them, dulling the whites etc.
There is, in my opinion, no cheap way to protect pastel drawings, but I do have two suggestions.
Find cardboard boxes with clear plastic inserts, like gift boxes where you can see inside them.
Take a high resolution photo and print them at the local drugstore or at an online service. Frame them as you would any photo.
The second option is probably the only way to cheaply conserve your pastel.
Glassine is used for protecting drawings, prints, etc while shipping or storing them, and not for displaying them. The proper way to permanently frame and display your artwork would be the one suggested by @Nothingismagick.
The cheaper alternative to glass that I know of is Plexiglass.
I'm not sure in what way you want to protect your art with plastic. If you want to package it so it can be seen and sold, you can get crystal-clear bags from clearbags.com. I've purchased from them and been very satisfied. They have a wide range of sizes. As "Nothingismagick" said, pastel art requires more protection than this, but watercolor, acrylic, thoroughly cured oil painting, colored pencil, and most other mediums should do fine in these bags. They really show your work to advantage.
If you're looking for an alternative to glass in framing, then you want some kind of plexiglass. In most cases the best place to look for this is in your local (preferably smallish) hardware store. This isn't likely to save you money since the better plexi-type glass alternatives are not cheap. However, it does have the advantage of not being so fragile (though most of it is easily scratched).
If you're trying to find a less expensive way of framing your watercolor or other fragile work (but NOT pastel--whether chalk or oil), it is possible to spray your artwork with an archival varnish.
Spray both sides, and keep coating it until it repels water on both sides. If you want to end up with a matte finish, use matte varnish ONLY for the final coat, as it will slightly obscure the artwork--not noticeable with one coat, but with many coats it will be unsatisfactory.
Ideally you would use a watercolor board as opposed to a flexible paper, or if you do use paper, you will need to mount it on archival foam board or other lightweight, rigid, acid-free backing--but you were going to do that before framing anyway. Watercolors, charcoals, pencil or colored pencil, or similar mediums treated in this way can be framed without matting or glass because they can be gently wiped clean with a damp cloth.