Technically speaking, I don't "need" the wide apertures very often. A couple of notable exceptions include indoor event photography (where the 35mm lens is my go-to choice) and indoor basketball (where, for now, the 50mm f/1.4 fills that need). I almost never use the 50mm f/1.4 at f/1.4, though - it just isn't sharp enough for my taste.
I'm hoping the Sigma 50mm f/1.4's AF is as good as the Canon. If so, I'll definitely be using it for indoor basketball among other things.
Another way I like to use relatively wide apertures is portraiture. Just last night Amanda and I did some shooting on the street that I live on. I used the Canon EF 85mm f/1.2 L II with a Singh-Ray Vari-N-Duo to allow me to achieve a relatively slow flash sync speed while still using a wide f/2.5 aperture.
A hint of fill light on the left side (to illuminate the inside of her hair) would have been optimal. But I was trying to keep the lighting simple with a single monolight diffused by a Mola Demi. Oh well...we got some other decent shots too.