My spouse has celiac disease an an uncompromising vegan so I routinely work around those restrictions.  I am sure we make many substitutions, but not many come to mind at the moment. 

I have found that gluten free flour mixes (both store-bought and ones we have mixed) work well as  one to one sub in many dishes.  Not long ago we made a vegan GF cake with vanilla buttercream icing (vegan butter) and it was surprisingly good.  The texture was less than ideal, but it wasn't terrible.  The GF flours have also worked very well in batter-dipped fried food (General Tso's cauliflower).

As kayb said, many off the shelf Asian sauces contain gluten and often it is used in/as the thickening agent; however, many sauces also contain soy sauce and it usually isn't gluten free.  Fortunately, those sauces can often be created from scratch using gluten-free soy sauce or tamari.  Doubanjiang (Sichuan/Pixian broad bean paste) has been tough to work around - especially in something like mapo tofu where it is prominent.  We usually substitute some combination of whatever GF Asian chili sauce(s) we have handy, fermented black beans and/or fermented bean paste (homemade). Gochujang is an option when the sweetness doesn't clash with the dish. 

When I am at the Asian market, I stock up on various rice noodles on hand as they can often be subbed for wheat noodles.  Of course it often isn't quite the same, but it is usually OK - especially in Asian dishes.