I think just about every man realizes how important testosterone is. It is not much of an exaggeration to say that testosterone affects everything in us guys, and I show you just how true that is below. Furthermore, low testosterone levels can increase risk factors for a host of nasty diseases and conditions, something I outline in my page on Hypogonadal Testosterone Levels.
So let's look at the profound effect that testosterone has males:
1. Cheat Death. Several studies have shown that low testosterone men have higher death rates.  The reasons for this will become very obvious when we cover the health benefits of reasonable testosterone levels below.
2. Red Blood Cells. Testosterone affects, of all things, your red blood cell counts. One of the proofs of this is the fact that low testosterone men are very often anemic. Another is the fact that men on HRT (testosterone therapy) have to have their red blood cell counts monitored. And it all makes sense, because testosterone affects red blood cell production through a "backdoor" pathway. It alters a renal hormone called erythropoietin that is responsible for triggering stem cell involvement in the bone marrow.
3. Arterial Stiffening. We all want nice, flexible arteries, especially below the belt, eh? Nice, flexible arteries allow for greater blood flow and lower blood pressures. For reasons not completely understood, low testosterone increases arterial stiffness and giving a man testosterone therapy can undo a significant amount of arterial stiffness.  Few men know of testosterone's "artery-softening" potential. This is something I cover in more detail in my book Low Testosterone by the Numbers.
4. Subcutaneous and Visceral Fat. Various studies have shown that as testosterone lowers both total fat and deadly visceral fat increase. One of the most interesting studies was on young men and showed a dose dependent loss of fat with increasing testosterone.  Other studies have verified the same thing. Many men struggling with weight don't realize they are actually struggling with hormones.
5. Venous Leakage. Can't maintain your erections? It could very well be because you have a condition called venous leakage where penile tissues cannot trap the blood flowing in the penis during an erection. This can lead to quickly disappearing erections or the inability to even achieve an erection. For more details, see my link on Venous Leakage.
6. Quasi-Senility. Testosterone is VERY important for brain function. Many studies have shown that it controls and influences various types of memory and mental processing. Here I will just mention that one study found that low testosterone actually turned men into quasi-senile seniors.  Of course, I don't mean it gave them literal Alzheimer's. However, the study did show that the men literally performed like an old man with dementia. Many men with classic low T symptoms can attest to how their hypogonadism has affected their careers, simply because they could no longer process information like they used to.
7. Muscle. This scarcely deserves a mention, because it is so well-known, but testosterone is definitely the "Muscle Hormone" and many studies show it to be just that. You don't have to have steroid levels to put on muscle - even a modest amount will do. However, many studies have shown that testosterone will help add muscle. In fact, it is so powerful that testosterone therapy has been shown time and again to add muscle to senior men. Yes, it's a wonder worker to your physical appearance.
8. Blood Flow and Nitric Oxide. One thing that few men know is that testosterone actually increase nitric oxide and blood flow levels in men. The increase can be quite substantail. In fact, one study found that the difference in blood flow between the lower and higher quartiles by testosterone was well over double!  And, yes, this means testosterone is important to your erectile strength.
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9. Insulin and Blood Sugar. What does testosterone do? Well, probably the most important is its governance of insulin levels. Of course, exercise and diet play major roles as well, but testosterone is one of the Big Three. Many studies have shown this directly and indirectly and that both blood sugar and insulin levels rise with falling testosterone. 
10. Inflammation. "Inflammation is the root of all evil." (Insulin is a close second in the evil category.) This statement is close to true being responsible for the Big Three Killers of men: heart disease, cancer and autoimmune disease. (Yes, you do need some inflammation for immunity, tissue repair, etc.) Probably the most infamous of the inflammatory cytokines, as they are called, is a signaling molecule called TNF alpha. TNF alpha has been implicated in many nasty medical conditions from arteriosclerosis to arthritis to Alzheimer's. And, as you may have guessed, low levels of testosterone have been shown to be associated with increased TNF alpha levels. 
11. Libido. Testosterone is the "passion hormone" for us men and researchers have verified that, in general, the higher the testosterone, the greater the libido and vice versa. In fact, men that are low testosterone will quite often write into The Peak Testosterone Forum saying that their libido has essentially vanished. They literally will feel castrated and without sexual desire whatsoever.  And, of course, this is almost always a startling contrast with their younger days when that is all they could think of!
12. Prediabetes. The hallmark of prediabetes is insulin resistance and rising insulin levels and - you guessed it! - lower testosterone are linked with approximately doubled risk for prediabetes.  This is, of course, because of the relationship presented in #8.
13. Diabetes. This is one of the reasons that men with low T have over double the risk of developing diabetes! Furthermore, I recently talked to the P.A. at a HRT clinic and every one of their type II diabetic men on testosterone was able to completely get off of insulin. Some still had to stay on Metformin, but, still, this will yield a huge improvement in blood sugar control and an increase in quality of life. One can't help but wonder how many cases of Type II diabetes could be completely eliminated simply through testosterone therapy.
14. Nocturnal Erections. There are many factors in achieving those all-important nocturnal erections, but one of the most important is having adequate testosterone levels.  To understand their criticality to penile health, see this link on How to Maintain or Rebuild Your Morning Erections. I have noticed that I get morning erections when my testosterone levels are greater than 600 ng/dl. Not everyone is the same on this, but this seems to be the levels that I need, and this is why testosterone cypionate really made the difference for me in this area.
15. Arterial Plaque. If there is anything that has greater importance than your arteries, I don't know what it is. Low testosterone appears to be an independent risk factor for atherosclerosis, or the infamous buildup of arterial plaque that clogs arteries and contributes to heart attacks and high blood pressure. One study of seniors verified this and found arteries significantly more clogged in hypogonadal men independent of other known cardiovascular risk factors. 
16. Sleep. Several studies have shown that, as testosterone levels fall, male sleep quality is lowered. In other words, low testosterone can actually negatively alter the stages of sleep. 
1) Circulation. 2007; 116:2694-2701, "Endogenous Testosterone and Mortality Due to All Causes, Cardiovascular Disease, and Cancer in Men"
2) Eur J Endocrinol. 2009 May;160(5):839-46. Epub 2009 Jan 27, "Effect of testosterone replacement therapy on arterial stiffness in older hypogonadal men"
3) Am J Physiol Endocrinol Metab, 2001 Dec, 281(6):E1172-81, "Testosterone dose-response relationships in healthy young men".
4) Oregon Health & Science University. "Testosterone Deprivation Makes Men Forget."ScienceDaily, 22 Oct. 2004. Web. 23 May 2011
5) Hypertension Research, 2007, 30:1029 1034; "Low Testosterone Level Is an Independent Determinant of Endothelial Dysfunction in Men"
6) "Androgens, Insulin Resistance and Vascular Disease in Men: Testosterone and Insulin Resistance", http://www.medscape.com/viewarticle/512077_4; Table 1
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8) The Journal of Clinical Endocrinology & Metabolism, Jul 1 2006, 91(7):2509-2513, "The Relationship between Libido and Testosterone Levels in Aging Men"
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10) Journal of Andrology, 18(5):522-527, "Relationship between sleep-related erections and testosterone levels in men"
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12) J Clin Endocrinol Metab, 2008 July, 93(7):2602 2609, "The Association of Testosterone Levels with Overall Sleep Quality, Sleep Architecture, and Sleep-Disordered Breathing"