There was a very interesting and important study that came out in 2010 almost unnoticed from the New England Journal of Medicine. These fine scholars asked the question, "What is the strongest predictor of middle and senior age hypogonadism ("male andropause")?
One of the reasons I find this study so fascinating is that there are SO many doctors out there who still think that low testosterone makes little difference. I get letters all the time with horror stories from guys who have struggled for years while their doctor completely ignored (or didn't know how to handle) their problem.
The study authors found that there were really only three key predictors of hypogonadism.  Notice that all three were sexual in nature. I list them below:
This means that low testosterone should simply be called The Great Sex Life Killer: it removes sexual desire, makes you limp and destroys the long term health of your penis by reducing morning erections. What's left, eh? And, if you've read my site at all, you know that Sex is Very, Very Good for Males, regardless of age.
So here's the bottom line, at least according to the study: if you have the above symptoms, you should ask to get tested for low testosterone since these are by far the most strongly correlated. Of course, I cover some of the other studies in my link on Low Testosterone Symptoms, but according to the NEJM, your sex life is the best indicator.
Furthermore, realize that doctors are often reluctant to identify and treat low testosterone. Consider this fairly recent 2007 study where the researchers 1) defined low testosterone as total below 300 ng/dl and free below 5 ng/dl.  These are very low numbers and guys will very often experience problems in the 300's and even 400's in some cases.
The study authors go on to argue, subtly, that many guys with low testosterone do not "complain", i.e. don't report the classic symptoms. To me this is dangerous thinking. Don't a lot of cancer patients report notice their cancer in advanced stages? Don't we all have different thresholds of pain, suffering and symptomatic difficulties? Guys are taught all their life not to complain - is it any wonder some of them don't talk about symptoms relating to low testosterone?
This is also what I find disturbing about the study. The researchers had a Clinical Practice Guideline from the Endocrine Society that had the following very rigorous guideline for treating low testosterone or hypogonadism:
Low total and free testosterone plus the presence of
plus two or more of the following symptoms:
This seems much too conservative to me. I mean you might as well just say that you don't want to treat hypoganadism, because you've set the testosterone level astronomically low, required osteoporosis and other questionable and ill-defined symptoms before you treat. I ask the question:
If a guy has a couple of low testosterone readings, what else do you need, especially considering the many dangers of low testosterone, including increased risk of Metabolic Disorder, heart disease and Diabetes?