The answer is yes, and you can play with them at [MoMath](http://momath.org/). Specifically, the [Twist and Roll]() exhibit has several convex shapes, which will roll arbitrarily far sideways when started at an angle that is not directly downhill.  

![](http://1.bp.blogspot.com/-PTwGQo4rOjU/UM_aXhScXOI/AAAAAAAACX0/zZ_mCIxQLuk/s1600/M26.jpg)

See also this [video](https://www.youtube.com/watch?v=L_z04poueUA), which shows the motion of several of the objects.