Motivated by Bott-Taubes integration, which utilizes integrals over configuration spaces in order to define finite-type invariants for knots, we explore the construction of invariants for vector fields on domains in $R^3$. As our underlying example, we aim to understand the helicity of a vector field, which measures the extent to which its flowlines coil and wrap around one another, and is related to the linking numbers of curves. Helicity is invariant under one-parameter volume-preserving diffeomorphisms of the domain; we provide a new proof of this using configuration spaces. Further, this definition of helicity generalizes to certain 2-forms; there, the volume-preserving requirement is unnecessary: helicity of forms is a diffeomorphism invariant. We conclude with another example: computing, via configuration spaces, a three-term analog of helicity for three unlinked solid tori.