Greetings from Phoenix!
It seems the reading community posting here is full into the latest trend... science fiction and fantasy. If you want to read excellent short stories about normal people in their normal lives, read anything by Joyce Carol Oates. She has published several short story collections in addition to her fantastic novels (We were the Mulvaneys, Missing Mom, etc.). I would suggest starting with High Lonesome: Selected Stories 1966 - 2006, available through EdwardRHamilton.com, a wonderful book discounter.
Her other short story collections are:
Upon the Sweeping Flood (1966)
The Wheel of Love (1970)
Marriages & Infidelities (1962)
The Goddess and Other Women (1974)
A Sentimental Education (1980)
Last Days (1984)
Raven's Wing (1986)
Heat (1991)
Will You Always Love Me? (1996)
Enjoy!