There are a number of options available, made from different polymers:

Recycled PET Reusable Bag

• It looks and feels like a fabric bag but is made from plastic (PET#1 bottles recycled into fabric, e.g. Loblaws' resuable bag)
• Recycled PET is a durable, eco-friendly fabric made from post-consumer recycled plastic bottles and containers 
• Reusable bags made from recycled PET create a market for post-consumer recycled materials

  Advantages

• Using recycled PET materials reduces waste and conserves a non-renewable resource  
• Strong and durable
• Requires 2/3 less energy to manufacture products made out of PET
• Can be blended with other fabrics, like hemp or polyester to make a nice material for reusable bags

Disadvantages

• Typically manufactured off shore
• Recyclable, but not currently in Canada
• Not recommended for machine washing (hand wash only)

Polypropylene Reusable Bags (PP)

• Made from spun, bonded, non-woven polypropylene 
• Non-woven polypropylene is a form of plastic—a flexible resin polymer used to make rope, chairs and the tops of Tic-Tac containers 
• This type of bag is very popular in Canada because of its strength and slightly rigid, sturdy profile 
• A semi-rigid insert is put into the bottom of the bag to provide stability

Advantages

• Very strong and durable
• Can be made from recycled materials
• Easy to wipe clean
• Wide variety of material color and printing options

Disadvantages

• While recyclable, it is not recyclable in Canada
• Made off shore
• Not biodegradable or compostable
• Made from a non-renewable resource
• Not recommended for machine washing (hand wash or spray clean only)
• Problems with lead in the inks and bag bottom inserts have led to a number of recalls
• Needs to be washed regularly to prevent bacterial cross contamination of food

Nylon Reusable Bags

• Nylon is a type of synthetic polymer originally made to replace silk in fabrics 
• Material compacts into a small ball for storage and ease of use

 Advantages

• Nylon is strong and durable
• Lightweight material
• Compacts easily
• Easily dyed which creates interesting material colour options
• Water resistant

Disadvantages          

• Not recyclable
• Slow to break down
• Made from a non-renewable resource
• Needs to be washed regularly to prevent bacterial cross contamination of food

http://www.allaboutbags.ca/typesofbags.html#nylon