As we point out often on this site, testosterone effects everything for us guys and, especially, the male brain. One of the surpising things that testosterone alters rapidly is mood. Yes, testosterone can make us guys "bitchy." In fact, believe it or not, researchers have a term for it: Irritable Male Syndrome. 
Researchers first noticed the effects of low testosterone in animals and have since studied this effect in a wide variety of mammals. What is counterintuitive is that instead of becoming docile and quiet, males with decreased testosterone become much more prone to fighting. Researchers noted that it could likely be due to a drop in brain opiods that are necessary for mood elevation. Thus they become both fearful and irritable at the same time - a toxic combination by any standards. (Think of that next time you make fun of a woman with PMS, eh?)
So just what do researchers mean by "mood?" Generally, questionaires are used and monitor psychological items such as "positive mood responses (alert, friendly, full of energy, well/good feelings) and negative mood responses (angry, irritable, sad, tired, nervous)."  Other studies have looked at similar attributes, such as "angry, alert, irritable, full of pep (energy), sad/blue, tired, friendly, nervous, and well/good." 
However, changes in mood parameters such as this are generally only experienced by men with hypogonadal testosterone levels. Several studies have shown that men with normal or even low normal testosterone levels experience little to no benefit in this area from testosterone therapy for example.  Young, healthy males may be more resilient as well to low testosterone according to one study, although the researchers found that they had "hot flashes" and were "emotionally charged."  Can you say PMS?
The evidence is quite clear, though, that low testosterone significantly affects mood in hypogonadal males.  And multiple studies using testosterone therapy have shown that it affects mood favorably.  Furthermore, it is also worth noting that several studies also show that mood improves rapidly in a matter of days or weeks rather than months. For example, one study on Androgel showed that almost all the improvement in mood happened within 30 days in men on Androgel.  And Androgel is not known for really pushing one's testosterone levels that high. Men on injections or pellets will undoubtedly feel even stronger and more rapid elevations in mood.
As a side note, you can, in fact, swing the pendulum too far the other way: researchers have actually increased testosterone to supraphysiological (abnormally high) levels and some of the men displayed signs of hypomania, i.e. symptoms such as euphoria and hypersexuality.  And I have heard this from an HRT clinic: if they go too high with a man's testosterone, he gets "amped" as the clinician put it and can lose their temper easily, etc.
The main point, though, is that raising one's testosterone, either naturally or through HRT, can be a definite mood-booster. On The Peak Testosterone Forum I find this to be the one of the most common benefits of going on testosterone. Men describe the incredible change to their mood and attitude from HRT (Hormone Replacement Therapy). Look at just a few of the comments:
"I am on day 25 and have lost over 24 pounds and feel like I am living again.I feel better than I have in years. Having spontaneous erections again, more energy and a better emotional state." 
"I'm also much "calmer" than before and mind seems better able to focus. You would think Raising T levels would make you prone to anger and violence? But it has had the opposite effect on me." 
"I am still taking my 1cc of 200 ml of Testosterone Cypionate a week and .5mg-1mg daily dose of Armidex. My next follow up blood work is in February. Words cannot describe how I been but in one word it will have to be INCREDIBLE. I make love to my wife on an average 6-8 times a week. I am taking advantage of this feeling because I never had it before and I am 34 years old. I love it. I am finally at the point where my wife has had enough in the bedroom and I am asking for more. This is the first in my life I ever felt so good and confident." 
(See this link on Hormone Replacement Therapy (HRT) for more information on testosterone therapy.)
Hopefully, the above quotes are a few real-life examples that show you just how important testosterone can be to mood. No, it is not a silver bullet that always works, but it is very often a major player. One of the sign that is a root cause of many mood disorders is the very recent recognition by the practicing medical community that correcting endocrine issues, especially testosterone, can greatly help with depression.
Physicians and those in the mental health fields suddenly noticed that a substantial percentage of depressed men were low T and giving them testosterone helped very often. The subject of Testosterone and Depression is so important that I did a page on it and documented the many kind of depression and mood conditions that HRT can help with. In my opinion, if a man is struggling with depression, one of the first numbers that should be pulled is testosterone.
1) Reprod Fertil Dev, 2001, 13(7-8):567-76, "The irritable male syndrome"
2) Maturitas, 2005 Feb 14, 50(2):124-33, "Effect of oral testosterone undecanoate on visuospatial cognition, mood and quality of life in elderly men with low-normal gonadal status"
3) Arch Gen Psychiatry, 2004 Oct, 61(10):997-1004, "The effects of pharmacologically induced hypogonadism on mood in healthy men"
4) The Journal of Clinical Endocrinology & Metabolism, Aug 1 2000, 85(8):2839-2853, "Transdermal Testosterone Gel Improves Sexual Function, Mood, Muscle Strength, and Body Composition Parameters in Hypogonadal Men"
5) The Journal of Clinical Endocrinology & Metabolism, May 1 2004, 89(5):2085-2098, "Long-Term Testosterone Gel (AndroGel) Treatment Maintains Beneficial Effects on Sexual Function and Mood, Lean and Fat Mass, and Bone Mineral Density in Hypogonadal Men"
6) Archives of General Psychiatry, Feb 2000, 57(2), "Effects of Supraphysiologic Doses of Testosterone on Mood and Aggression in Normal Men"
7) J Clin Endocrinol Metab, 1996 Oct, 81(10):3578-83, "Testosterone replacement therapy improves mood in hypogonadal men--a clinical research center study"