There are a number of ultramarathons that are 100 miles (like the Western States 100 Mile Endurance Run), or are based on 24 or 48 hour time periods. There are some ultramarathons like Badwater that go a bit over 100 (that one is 135).
As to if something is really truly "non stop" -- as in zero walking, or rests, etc. -- is debatable, I suppose.
The longest certified endurance race is the Sri Chinmoy 1300-Miler, in which the participants have 51 days to cover the distance. (That makes an average of over 60 miles per day.)
The clock keeps running so it's technically "non-stop," but the participants obviously do periods of rest for a race that lasts almost two months.
Some runners such as Pam Reed and Dean Karnazes at one point claimed to be pursuing the longest non-stop run (without sleep) at distances of 300 and 350 miles. However, Yiannis Kouros supposedly covered 456 miles in 4 days in 1988 without sleeping at the start of ultimately covering 1000 miles.