1. This table runner by House of Earnest gives black burlap a graphic, modern look with hand sewn white crosses. (Also check out her tip for cutting the runner to size.)
2. Inexpensive, plain vases — or even tin cans — wrapped in burlap (and maybe some ribbon) make a pretty base for flower arrangements. Image by Cat Satre, via Style me Pretty.
3. Borrowing an idea from Real Living, trace around your plate, cut the burlap, and you have a very, very easy charger/placemat.
4. Love of Family and Home made napkin rings that are easily to replicate with cardboard (she used toilet paper rolls) and burlap. You can make them seasonal by adding pinecones, berries, evergreen sprigs, etc.
5. If you're more comfortable with a glue gun than a sewing machine, check out these no-sew utensil holders from I Heart Naptime.
MORE BURLAP ON APARTMENT THERAPY:
• DIY Jute Table Runner
• Simply Beautiful Burlap
• How to Make Coffee Bag Planter Pots
(Images: As linked above)
Small Cool Lessons: Discovering Small Space Design Ideas That Really Work
Beatriz's Fun and Functional Workspace
Good Food to Share 
The Big Book of Small, Cool Spaces 
Apartment Therapy Presents 
The Eight-Step Home Cure 
Sheex Bedding
A Work Week Menu Plan That You Can Do
How to Make Fresh Pasta Dough in the Food Processor
I'd probably buy that first runner if someone sold it...
Does anyone know where I can find neat looking burlap?
Burlap smells like a barn. Which, in my opinion, is the best place for it! ;^)
Thinking of wallpapering my entry/hall in burlap. I will let you know if I proceed.
Burlap can be purchased at fabric stores. By the yard, off a bolt or in the ribbon section for pre-cut strips. Most feed stores no longer carry burlap bags, they have switched to plastic.