Is there a definition for wavelength of a non-plane wave? For example, a wave with wavefronts that are not equally spaced from each other, is there a definition of wavelength?
 A: Before I give my answer, let's clear up some terminology here.

*

*A plane wave is a solution of the wave equation,
$$
\nabla^2 u = \frac{1}{c^2} \frac{\partial^2 u}{\partial t^2}
$$
of the form $u(\vec{r},t) = f(x - ct)$ for some Cartesian coordinate $x$.  It is so named because all of the points with a given $x$-coordinate have the same value of $u$ at a given time, and this set of points forms an infinite plane in space.  The function $f$ may be freely specified, and need not be a sine or a cosine.  For example, the function $u(\vec{r}, t) = e^{-(x-ct)^2/2 \sigma^2}$ is a perfectly valid plane wave solution to the wave equation, but it only has one peak;  it specifies a "pulse" wave, shaped like a Gaussian, traveling in the $x$-direction.


*A monochromatic wave is a wave for which all points in space oscillate at the same frequency, i.e.,
$$
u(\vec{r},t) = v(\vec{r}) e^{i \omega t}.
$$
It is not hard to see that this implies that the function $v$ satisfies the Helmholtz equation:
$$
\nabla^2 v + k^2 v = 0,
$$
with $k = \omega / c$.  Solutions to this equation do often have something like a well-defined wavelength $\lambda = 2 \pi / k$, but they do not necessarily have the form of plane waves.  For example, in spherical coordinates, the solutions to this equation are of the form $v(r) = A \sin (kr)/r$. The wavefronts are spheres, not planes, but they are spaced by $\lambda = 2 \pi/k$.
So the answers to your questions are:

Is there a definition for wavelength of a non-plane wave?

Sometimes.  It depends on the geometry of the solution.

For example, a wave with wavefronts that are not equally spaced from each other, is there a definition of wavelength?

No;  we can only talk meaningfully about "a" wavelength if the wavefronts are all equally spaced.  But note that a plane wave doesn't necessarily have its wavefronts equally spaced either.
A: A non-plane wave is a wave whose points of equal phase are not located on a plane in space. This has nothing to do with wavefronts not being equally spaced. Examples of non-plane waves are cylindrical (circular) or spherical waves where you can also define a wavelength if they are produced by periodic signals. Only periodic signals produce waves with a wavelength. Waves with unequal spaces between wavefronts correspond to signals that are not periodic. Therefore the distances between such wavefronts are not related to any wavelength.
