Assess whether the blown glass pieces you have can be used by someone else. If they are not broken or chipped, recycling them may actually consist of re-using them. Drop them off at a charity donation center like Goodwill or The Salvation Army, making sure to properly package them for the trip to the collection center. Get a receipt for your donation that you can use for a deduction at tax time.
Check out your local garbage and recycling hauler's rules for recycling glass. Often, you can recycle glass curbside by placing it in a separate container than the other recyclables. Check your hauler's website, or call on the phone if you're not familiar with the glass recycling process. If your blown glass is not broken, you may be able to place it in your glass recycling container, and then put it on the curb for pickup, depending on your company's policies.
Look for a collection center in your area, if you don't have curbside glass recycling that accepts your blown glass, or if your blown glass is broken. You can find collection centers all over the United States by typing your ZIP code into the searchable database at Earth911's website. Many centers do not accept glass containers and non-bottle forms of glass, because they may have been treated during processing, but check with them anyway. If they are willing to accept your materials, package them safely so they are not broken in transit, and take them to the collection center for drop-off during regular business hours. You may need to show identification to drop off materials at a municipal collection center.
Find a way to repurpose your glass, if you have no other way of getting rid of it. Since blown glass can come in many unique colors, you could break the glass into smaller pieces, tumble it in a glass tumbler, and use it to make jewelry. You could also use the bits of glass in a mosaic or mural.