Pretty metal clips
Clips like these from Liz's Antique Hardware in Los Angeles, add character; look for old clips at flea markets and antiques stores.
Rayon cording
Rayon cording tied through grommets gives a finished look; hide the knot behind the grommet.
Iron-on fusing tape
to create a channel wide enough for a rod or wood dowel to pass through.
Clip-on curtain rings
Clip-on rings are available through companies such as IKEA and Smith and Noble.
Buttons
Even with buttons you don't need to sew: Thread fine wire through buttons to connect loops of grosgrain ribbon to fabric.
Beaded loops
Team beaded loops, made from 24-gauge wire, with wall hooks for an easy fix. Poke a hole in the fabric with a straight pin and the wire will pass through easily.
Embellished wire
Thread beads on "memory wire" (wire coils that retain circular forms; available in bead shops) to make a simple curtain ring.