This year, my mother wanted to make me reusable cloth gift bags.  She had found one at some type of local art fair, and figured out how to sew them.  

We picked out printed fabric, used matching broadcloth as a lining, and then attached a ribbon at the seam near the top to wrap around and then tie them.  When she had me cut them out, I would fold the fabric over so that there was only a seam on one side of the bag and on the bottom.  I'm not sure exactly how she sewed them together, but if you sew, you might want to experiment.

I've been using a tag maker punch from my scrapbooking supplies to use as gift tags.  So far, they have been very well received.  Even my husband's male friends thought they were cool since they could use them to easily wrap a gift (or because I found fabric with their favorite sports teams...).  I haven't decided whether I prefer to give ones with holiday fabric or ones that can be used anytime.

I'd love to see a picture of these. They sound like a very neat idea!

They are not as pretty as the bags you described, but I made a dozen or so felt drawstring gift pouches for our household. I made them big enough for 3 DVD cases to fit in, as that will fit most DVD box sets, CDs, and many books. The felt is a bit plain in the solid colors, but it required less finish work. Because they are plain, we can use them for any occasion. 

My daughter made birthday bags from old jeans, bits of lace and colorful fabric scraps such as satin, taffeta, etc.  The children loved them.

My daughter received 2 cloth bags with birthday presents inside a few years ago.  They are about the size of a package of binder paper.  They are just made from cotton fabric, folded over, sewn up one side and across the bottom.  They are just folded in and hemmed at the top.  There's no ribbon sewn at the top, but I wish there was!  I just take a cloth ribbon to tie them closed.  I love them so much I have used them over and over again, but only for my immediate family because I don't want to let them go!  lol.  It's very simple sewing, any cheap cloth would work, and I really should just make some to give out with gifts to everyone.  Note to self:  add that to my to-do list...

My cloth gift bags are not fancy, but they're fun. Most are made from scrap fabric left over from the sewing my mom used to do 20 something years ago. Other stuff is remnants I've picked up at thrift/secondhand stores. When possible I try to get my ribbons that I sew onto them from similar sources.

I have made a few bags out of other things....one was from a pair of kids pajama pants that I found in the discard pile at the thrift store (too ragged at the hems for them to sell, but otherwise good) and from a pair of shorts. Also made a larger bag out of one of my gramma's old curtains.