When it comes to libido and sexual desire, you have no truer friend than testosterone. Study after study on rams, sheep, rats, mice and a lot of other animals have shown just how strongly testosterone and libido are related. I quite often get letters from wives saying things like, "My hubbie is lethargic, anxious and has almost no libido. Could that have to do with his low testosterone?" The answer, of course, is a definite 'yes'!
Many studies have shown that testosterone affects mood, cognition and mental function in men. Sexual desire is no exception. One urological journal summarized by saying that testosterone enhances libido, frequency of sexual acts and sleep-related erections.  "Enhances" is an understatement if we've ever heard one and that's especially true if you have low testosterone. Several studies have shown that low testosterone is a powerful desire-killer. 
Furthermore, several studies have also shown that testosterone therapy can have profound sexual desire-boosting powers in hypogonadal men. In fact, one of the most interesting ones was a study of low T senior men with erectile dysfunction. About half of them had their erectile dysfunction greatly improved through testosterone therapy. However, what is remarkable is that 100% of the men experienced dramatic improvements in libido from the testosterone.
NOTE: This same study showed that a significant percentage of men took 12-24 weeks to experience the effects. In other words, it takes time to rebuild receptors and tissues and if you "don't feel anything right away," that doesn't mean that nothing is happening.
Does HRT help everyone? Well, you can never say always. However, it has helped some categories that most would consider very tough to treat or cure. For example, diabetics who are non-responders to Viagra were helped significantly with sexual desire  as have HIV patients with normal testosterone. 
The one category of man that may not be helped much in the libido category are those who are not that low in testosterone. One meta-analysis found just this: men who were low testosterone were helped greatly and men with low-normal or normal testosterone only moderately.  Apparently, taking your testosterone from, say, 450 ng/dl to 700 ng/dl is going to have a much less noticeable effect and that makes some sense.
Other research, though, has shown a much more "linear" relationship between libido and testosterone. For example, one study of senior men showed that libido followed a nearly linear progression across all ranges of testosterone. . In this case, they took senior men between the ages of 60 and 75 and then reset their testosterone production almost to zero through a pharmaceutical GnRH agonist. They then gave these men varying dosages of testosterone and found that, in men that were sexually active, the more the testosterone, the greater the libido.
This is called "dose dependency" and is a sign that there is a strong correlation between two variables, in this case testosterone and libido. The study also found that waking erections and sexual function were also dose dependent.
Other studies have shown somewhat similar results. A study of community-dwelling seniors ordered men by a 14-point scale on libido and found that "analyses indicated a 3.4 ng/dl (0.12 nmol/liter) increase in total T per unit increase in libido."  So almost all men will find that their libido is influenced by testosterone, but those with low testosterone will likely have the most noticeable effect.
1) WORLD JOURNAL OF UROLOGY, 15(1):21-26, "The effects of testosterone on the cavernous tissue and erectile function"
2) Am J Psychiatry, 155:1310-1318, Oct 1998, "Age-Associated Testosterone Decline in Men: Clinical Issues for Psychiatry"
3) The Journal of Sexual Medicine, Mar 2007, 4(2):497-501, "Improvement of Sexual Function in Men with Late-Onset Hypogonadism Treated with Testosterone Only"
4) The Aging Male, Jun 2003, 6(2):94-99, "Oral testosterone undecanoate reverses erectile dysfunction associated with diabetes mellitus in patients failing on sildenafil citrate therapy alone"
5) Int J STD AIDS, 1998, 9:41-44, "Testosterone therapy for clinical symptoms of hypogonadism in eugonadal men with AIDS"
6) Mayo Clinic Proceedings, Jan 2007,82(1):20-28, "Testosterone Use in Men With Sexual Dysfunction: A Systematic Review and Meta-analysis of Randomized Placebo-Controlled Trials"
7) The Journal of Clinical Endocrinology & Metabolism, Jul 1 2005 90(7)7:3838-3846, "Dose-Dependent Effects of Testosterone on Sexual Function, Mood, and Visuospatial Cognition in Older Men"
8) J Clin Endocrinol Metab, 2006 Jul, 91(7):2509-13. Epub 2006 May 2, "The relationship between libido and testosterone levels in aging men"