Here is a simple, quick and attractive alternative to drilling holes in glass. This method can be scaled up and down to suit the size of the glass (or similar object) in question. Depending on your aesthetic choice, it can be strung through either the bridge in the middle or the top of the spirals.
Use reasonable caution: don't pinch yourself, stab yourself in the eye with flying wire bits, etc.
Step 1: Measure Your Wire.
How long the wire needs to be depends on how big the final spiral will end up. Using about 20cm of 2mm gauge copper wire, my spirals averaged about 1.5cm in diameter. Almost any wire will do for this, so long as you can get enough torque to bend it tightly.
Step 2: Grip It by the Husk
With some good treaded, narrow pliers, hold it very tightly in the middle.
Step 3: First Right Angle
Now bend the wire over the pliers, forming a right angle.
Step 4: First Spiral
Using that same grip, pull the end of the wire around sharply to make the center of a spiral. Continue bringing it around until you run out of bendable wire, and try to keep the spiral as flat and tidy as you can. Clip the un-bent end off, if you have one.
Step 5: Second Bend
Gripping as closely to the first spiral as you can, create another 90 degree angle. In order to keep it symmetrical, try to mirror the direction of the first bend.
Step 6: Second Spiral
Bring the wire around to create another spiral; follow the direction of the first one to keep it neat looking. Trim any extra end bits. If this piece is meant for jewelry, you may want to file down the sharp edges made by the cut.
Step 7: Attatchment
Fit the glass into the space created by the two spirals. You may need to bend the wire inward to create a 'pinch' to properly hold the glass. If you are confident in your spiral's pinching properties, then you are done! String it and admire your new suncatcher/earring/pendant/etc. If it seems a bit loose or you are expecting it to undergo jostling, a dab of glue might be a good idea. And if you make something from this idea, I would love to see it!