They are called "sneakers" but you're usually sneakier without them on...

Ked's purports to have coined the term in ~1916 (but can only prove to have used it from 1922 on), but shortly after launching theoriginalsneaker.com, came under scrutiny when they could not substantiate their claim. They soon edited their website to note that the term sneaker was coined by Boston schoolchildren, which has been validated by a New York Times article quoting a Boston schoolmaster in 1887.

Firstmention.com offers a similar validation, citing an article from 1889 for a Boston shoestore selling "tennis oxfords (sneakers)"

Etymonline, the online etymology dictionary, credits the term "...The night-officer is generally accustomed to wear a species of India-rubber shoes or goloshes on her feet. These are termed 'sneaks' by the women [of Brixton Prison]. ["Female Life in Prison," 1862]..."

sources: etymonline.com, newyorktimes.com (3/22/10)