Most hypogonadal men that go on HRT (testosterone therapy) expect it to ramp up their libido and erections almost right away. However, what happens more often is that the testosterone first affects their brain. I remember when I went on pellets, which got my testosterone levels up near 600 or 700. I noticed my (mild) anxiety and dysthymia improving significantly. And, when I went on testosterone cypionate, which boosted my testosterone further still, I could feel it right between the ears. The evening of my first shot I told my wife that it felt like my brain was being rewired. It took a few days for morning erections to begin and libido to rise. But the brain boosting benefits came right away.
So let's look at some of the key brain changes that researchers have noticed relating to testosterone:
1. Dopamine. Testosterone's most pleasurable effect on the brain has got to be it's dopamine-boosting powers. In my link on Testosterone and Dopamine, I document how there are key parts of the brain that are heavily dependent on T to boost dopamine and that dopamine is one of the keys for one's sex life.
Researchers have increasingly found that dopamine is also a huge key in fighting depression.  Many men have used Buproprion (Wellbutrin/Zyban) to overcome depression due its unique abilities to often help sexual function. How does Wellbutrin work? One of its modes of action is boost dopamine in certain important brain regions. Gotta have it!
2. Acetylcholine. Testosterone appears to boost acetylcholine, the "memory neurotransmitter" as well. One study noted that "gonadectomy selectively reduces acetylcholine in the hippocampus."  So low testosterone is not just hard on your sex life - it's hard on your brain!
NOTE: As a side note, this testosterone boost of acetylcholine is also probably good for your erectile strength. Acetylcholine is kind of "Nitric Oxide Lite" and helps with vasodilation. One animal study showed that testosterone boosted acetylcholine in the levantor ani muscle, which is part of your all-important pelvic musculature. 
3. Hippocampal Neurogenesis. Hippo what? Researchers recently found that exercise actually created new cells in the rat hippocampus, which is the center of memory.  The hippocampus is attacked by the plaques and tangles of Alzheimers for example.  Of course, this is HUGE and is an example of the "plasticity" of the brain and its ability to at least partially rebuild itself.
Okay, so exercise can rebuild the hippocampus. But what does that have to do with testosterone? Well, it turns out that testosterone plays an indirect role. Exercise boosts brain levels of testosterone - some of which is converted (via 5-alpha reductase) into DHT - and it is DHT which is responsible for the neurogenesis.
4. Vasopressin. Oxytocin's lesser known cousin, vasopressin regulates scores of activities in the body, including blood pressure, post-orgasmic response, memory and the CNS (central nervous system). Researchers have noted that rats lose their vasopressin-related nerve fiber in certain parts of their CNS when testosterone is lowered. And, when testosterone is restored, the nerve fiber density in these regions is restored.  This is yet another example where adding testosterone to a deficient animal is like watering a flower: whatever is wilted and about to die comes back completely to life. (Venous Leakage is yet another example.)
5. Memory. Many studies have shown that testosterone improves working memory in men.  And working memory is ground zero for just about everything that you do in your brain. Almost anything that needs to be processed has to go through working memory before it is analyzed, stored or synthesized by other parts of the brain. Other studies have shown that visual and verbal memory improve in men given testosterone.  No wonder that many hypogonadal men complain of "mental fog". Part of this may be due to testosterone's ability to stimulate acetylcholine, the "memory neurotransmitter" mentioned in no. 2.
6. Cognition. Yes, even your ability to think is affected profoundly by testosterone. Studies, for example, have shown that testosterone increases spatial processing power in both young and older men.  So, if you're looking for a nootropic AND you happen to be low T, testosterone may be your answer. It's ability to improve many types of memory and increase cognition is hard to beat. In fact, some executives are now going on HRT just because of its brain-boosting abilities. See my link on Testosterone for Executives in the Peak Testosterone Forum for more information.
Did you know you can inexpensively do your own testing for many hormones? The industry leaders is Discounted Labs..
NOTE: According to one study, DHT did NOT improve working memory.  That is suprising considering its powers over the hippocampus mentioned in #3.
7. Depression. One of our biggest health problems is depression. This afflicts tens of millions of men worldwide every year. Of course, the standard treatment for years was to throw truckloads of SSRI's at the problem, which have had tepid results at best. However, researchers are finally recognizing that in men with lowish testosterone, HRT can often greatly help. One meta-analysis found that "TT may have an antidepressant effect in depressed patients, especially those with hypogonadism or HIV/AIDS and elderly subpopulations."  What is remarkable is that this study was willing to go on record and state that "the route by which TT [testosterone] is administered may play a role in treatment response." in other words, they actually admitted that testosterone can have a place in proper treatment of depression (in men with low or lowish T). For more information, see my link on Testosterone and Depression.
8. Anxiety. Hypogonadism and high anxiety very often go together as I show in my link on Testosterone and Anxiety.
9. Gherlin. Gherlin is famous as the "Appetite Hormone" but could just as easily be thought of as a Brain Hormone because it plays such a pivotal role in the health of your key memory brain structure, the hippocampus. It turns out that being low testosterone leads to low gherlin levels and HRT (testosterone therapy) restores gherlin levels to baseline. See my link on Testosterone and Appetite for more information.
CAUTION #1: According to famed oxytocin researcher Paul Zaks, testosterone is an oxytocin inhibitor.  Of course, oxytocin is the "Bonding, Empathy and Generosity Hormone" and so, according to his research, increasing testosterone could make one less empathetic, which obviously is not a good thing. I think one has to be cautious with jumping to conclusions here for men with reasonable testosterone levels. There is also considerable research that shows that it is the low testosterone males that are anxious and more likely to fight and be aggressive. It does point out, though, that more not always be better.
One thing I have wondered, though, if this oxytocin-inhibiting property of testosterone is not partially ameliorated by the fact that, at least in animal studies, testosterone increases oxytocin binding.  One study even noted that castrated animals lost their oxytocin receptors in certain key brain regions and restoring testosterone brought back oxytocin receptors to youthful levels.  Oxytocin may also have a dark side: researchers have found that it can increase envy and gloating.
CAUTION #2: One can make the argument that testosterone should be ramped up slowly rather than starting high and "seeing what happens" as is almost always the case. An example of this was one of our posters on The Peak Testosterone Forum that experienced an almost manic episode after going on testosterone pellets. This is a rare reaction, but it probably ties back to testosterone's brain-boosting abilities. If a man is hypogonadal and suddenly triples his testosterone through HRT, that's a lot of adjustment for the brain to handle in some cases all at once.
1) Fundamental & Clinical Pharmacology, Dec 2004, 18(6):601-607, "Dopamine, depression and antidepressants"
2) Trends in Cognitive Sciences, Feb 2006, 10(2):77 82, "Thinking with your gonads: testosterone and cognition"
3) Journal of Neurobiology, Mar 1982, 13(2):153 161, March 1982"Testosterone increases acetylcholine receptor number in the levator ani muscle of the rat"
5) Neuroendocrinology, 1989, 50:199 203, "Testosterone Modulates Oxytocin Binding in the Hypothalamus of Castrated Male Rats"
6) Brain Research, Feb 1998, 1(23):167 170, "Region-specific effect of testosterone on oxytocin receptor binding in the brain of the aged rat"
8) Brain Research, Mar 1990, 511(1):129 140, "Gonadal steroids regulate oxytocin receptors but not vasopressin receptors in the brain of male and female rats. An autoradiographical study"
9) Brain Research, Nov 1988, 473(2):306 313, "Testosterone supplementation restores vasopressin innervation in the senescent rat brain"
10) Journal of Cognitive Neuroscience, May 2000, 12(3):407-414,"Sex Steroids Modify Working Memory"
11) Experimental Neurology, June 2003, 181(2):301 312, "Testosterone, but not nonaromatizable dihydrotestosterone, improves working memory and alters nerve growth factor levels in aged male rats"
12) Neurology, July 10 2001, 57(1):80-88, "Testosterone supplementation improves spatial and verbal memory in healthy older men"
13) Aging Male, 2006 Dec, 9(4):195-9, "Testosterone and the brain"
14) Arch Gen Psychiatry, 2006 Feb, 63(2):161-7, "Increased hippocampal plaques and tangles in patients with Alzheimer disease with a lifetime history of major depression"
15) Proc Natl Acad Sci U S A, 2012 Aug 7,109(32):13100-5, "Mild exercise increases dihydrotestosterone in hippocampus providing evidence for androgenic mediation of neurogenesis"
16) Journal of Psychiatric Practice, Jul 2009, 15(4):289-305, "Testosterone and Depression: Systematic Review and Meta-Analysis"