Some vector-valued functions that generate helices:

ParametricPlot3D[ { Cos[t], Sin[t], t }, {t,-2Pi, 2Pi} ]

ParametricPlot3D[ {Cos[4*t], Sin[4*t], t }, {t,-2Pi, 2Pi} ]

Some examples students found interesting while exploring the idea:

ParametricPlot3D[ {Tan[t], Sin[t],Cos[t]}, {t,-20,20}]

ParametricPlot3D[ {t^2, Cos[20t],t}, {t,-2Pi, 2Pi} ]