Very short answer: for a comprehensive reference, you can't beat Hairer and Wanner volume II.
Short answer: Here are some MATLAB scripts to plot the stability region of a linear multistep or Runge-Kutta method, given the coefficients. You could also use the Python package nodepy (disclaimer: it's my package and it's not the most polished piece of software, but plotting stability regions is one thing it does very well). Instructions for plotting stability regions are here.
Longer answer: there are three classes of methods you could be interested in here.
$A$-stable methods, where all of the left half of the complex plane lies in the stability region. The most well-known examples are backward Euler (1st order) and the implicit trapezoidal method (which is what Crank-Nicholson uses). For these methods, you don't need to know the details of the stability region; as long as the eigenvalues of your spatial discretization lie in the left half-plane, you'll have unconditional stability (no step size restriction). Due to the second Dahlquist barrier, you have to use Runge-Kutta methods if you want high order and $A$-stability. Some examples of such methods are the Gauss-Legendre, Radau, and Lobatto methods. All of those are fully implicit and thus rather expensive.
$A(\alpha)$-stable methods, which include a sector in the left half-plane, including all of the negative real axis. The most prominent of these are the backward differentiation (BDF) methods and a variant known as "numerical differentiation formulas", which are implemented in MATLAB's ode15s(). These are unconditionally stable as long as the eigenvalues of your spatial discretization lie in that sector, so the only thing you need to know about the stability region is the angle $\alpha$, which you can find in any reference on ODE solvers (for instance, p. 175 of LeVeque).
Explicit methods, which will necessary include only a finite interval on the negative real axis. There are special "stabilized" explicit methods (in particular, the Runge-Kutta-Chebyshev methods) that have large negative real axis stability regions and are suitable for mildly stiff problems, but usually not for parabolic problems. A good entrance to that literature is this paper, which includes lots of information about the stability regions.
I've assumed throughout that you're only interested in absolute stability. For parabolic problems you would likely want an $L$-stable method as well, but it's simple to check $L$-stability of a method.
Update: If you really need to know everything about this topic, get a copy of Dekker and Verwer's monograph. It has one of the best existing introductions to concepts like one-sided Lipschitz constants, the logarithmic norm, and several deeper stability concepts. It's out of print but you can usually find used copies on Amazon (for a price!)
