I am looking for an easy to implement stabilization scheme that can be used with equal order ($P_1-P_1$ or $Q_1-Q_1$) finite elements for fluid flow. Is there something like this or should I stick to Taylor Hood elements? It appears that there are a number of methods but the ease of implementation is not quite clear.
First, be warned that stabilization is generally much more fragile than use of stable elements. If you solve a narrow class of problems, you might be able to choose reasonable parameters and get on with your work, but if you solve a wide range of problems or need to solve demanding under-resolved scenarios, especially with less regular boundaries, coefficient structure, and constitutive relations, stabilization will generally require constant vigilance to detect and quantify the impact of numerical artifacts, and to re-tune parameters for.
For these reasons, I strongly recommend stable elements (especially those with discontinuous pressure space, thus locally conservative) if you want a robust method that does not need to be frequently revisited. In my opinion, reliability and clean analysis is worth the modest increase in data structure complexity.
I'll outline the two most popular choices in the context of a stabilization term $S_h(\mathbf u_h, p_h, \mathbf f; \mathbf v_h, q_h)$ to be added to the weak form.
This is a late response, but I want to point out the option (for the time-dependent case) of using a pressure-approximation type of projection method, based on solving a Poisson equation for the pressure with a well-posed boundary condition. See  for derivations and tests, including tests with equal-order finite elements.
I have to admit that Jed Brown's warning still largely applies, however --- the schemes proposed and discussed in  appear very flexible and are supported by some theory and some testing, but have not been widely tested on many different problems. They may prove to be robust, but this has to be proved by experience.
 J.-G. Liu, J. Liu, R.L. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, J. Comp. Phys. 229 (2010) 3428-3453.