I wear Rx orthotics for flat feet and to slow down the development of a bunion.
My podiatrist made two pairs for me: one for athletic shoes, and a thinner profile pair that can fit in most, but not all, casual/dress shoes. There is a circle cut out of the heel of the dress orthotics so they sit flatter in the shoe and don't lift my heel up too much.
I actually use the dress orthotics in some of my athletic shoes... they fit in my cycling shoes, and I've decided that I like them better in my ski boots than the pair that was made for athletic shoes.
There are some really great casual shoes out there that can be compatible with your orthotics, or if they're not, just limit how often you wear them or save them for special occasions.
2014 Bobbin Bramble / Brooks B67
2008 Rodriguez Rainier Mirage / Terry Butterfly Tri Gel
2007 Dahon Speed Pro TT / Biologic Velvet