Well, like I always say: "Testosterone affects EVERYTHING in men."
Sure, that's an exaggeration. But not by much and a great example of that is blood pressure. A muscle-building, libido-increasing hormone androgen like testosterone might seem completely unrelated to arterial blood pressure but nothing could be further from the truth. Testosterone not only can lower your blood pressure a little in the short term but can definitely protect it long term and the studies show this quite clearly.
Now we'll discuss just why in more detail, but let me say that if you have hypertension (or prehypertension), testosterone is not going to be a miracle cure for you. Getting your testosterone to respectable levels will probably help though, but for much more powerful solutions, see my pages on Natural Ways to Lower Blood Pressure and How I Lowered High Blood Pressure.
CAUTION: It is important to mention that a side effect for a small minority of men on HRT (TRT) is elevated blood pressure however. Many doctors do not realize this, so get him or her measuring your blood pressure.
However, if your testosterone is low and you boost it sufficiently, you can lower your blood pressure. The reason is that testosterone boosts the activity of eNOS (endothelial nitric oxide synthase) and, if you'll recall, eNOS is the same enzyme that Viagra and Cialis affect. While testosterone does not have as powerful of an effect as these pharmaceauticals, it does make a difference. And this effectively means higher nitric oxide levels which means more relaxed arteries and lower blood pressure.
Is there any evidence for this phenomenon? One 1988 study found that the higher the testosterone, the lower the blood pressure. Of course, the first thing one might suspect is that the this relationship had only to do with the weight of the participants of the study. However, the researchers had the foresight to look at this and found that not all of the decrease in blood pressure with increasing testosterone could be explained by BMI (obesity levels).  A follow-up study year later verified the same result: testosterone was strongly correlated with blood pressure and only part of it could be explained by extra body fat levels. 
One test that researchers have done is looking at the reverse direction, that is whether or not testosterone therapy can improve blood pressure. If testosterone impacts blood pressure directly, then lower testosterone men who receive HRT should find their blood pressure lowered. One older (1992) study on obese men receiving testosterone therapy noted that "insulin resistance ... improved and blood glucose, diastolic blood pressure and serum cholesterol decreased." 
A follow-up study a few years later found similarly remarkable results, which included "decrease of visceral fat mass..., by increased insulin sensitivity..., by a decrease in fasting blood glucose, plasma cholesterol and triglycerides as well as a decrease in diastolic blood pressure." 
Notice the incredible changes in multiple cardiovascular risk factors that were improved with testosterone therapy, including the lowering of blood pressure. Blood pressure is dangerous to many tissues of the body, because even small increases can lead to "scarring" of arteries and damage to smaller blood vessels and even connective tissue. The kidneys, eyes and brain are very vulnerable and often incur long term damage.
NOTE: See my link on Hormone Replacement Therapy for more information on the pros and cons for men with low testosterone.
A more pronounced effects is testosterone's ability to protect men from high blood pressure and hypertension in the long term. The reason is simple: testosterone is inversely correlated with arteriosclerosis and hardening of the arteries.  Again, one might not think that testosterone would protect arteries, but that is, in fact, the case. Testosterone's ability to raise nitric oxide levels helps protect arteries. Just as important, it also 1) lowers insulin levels, which significantly reduces the risk for insulin resistance and 2) helps men maintain and even lose weight. Both #1 and #2 are good for the entire cardiovascular system and help prevent hypertension and prehypertension. It also can help prevent erectile dysfunction as well.
Did you know you can inexpensively do your own testing for many hormones? The industry leaders is Discounted Labs..
NOTE: Hormone levels, especially testosterone and estradiol, can powerfully affect a man's sex life and much of it centers around how this hormone affects our blood pressure: for more information, see my link on Testosterone and Erectile Dysfunction. Hormone levels, especially testosterone and estradiol, can powerfully affect a man's sex life and a little of it probably centers around how this hormone affects our blood pressure. In most men, testosterone will have a slight blood pressure lowering effect, raising nitric oxide, boosting libido and decreasing hardening of the arteries. Again, the biggest signs of low testosterone have been found to be sexual in nature, as I document in my link on Hypogonadism and Testosterone.
CAUTION: Not all researchers are as positive about testosterone and blood pressure. In fact, one recent study coming from the standpoint of the kidneys, which are front and center in the regulation of blood pressure, stated that "in sum, net effects of androgen action seem to be vasoconstriction, atherosclerosis and stimulation of the renin-angiotensin-aldosterone system." 
1) Journal of Hypertension, 1988, 6(4):329-332, "Blood pressure and endogenous testosterone in men: an inverse relationship"
2) Eur J Endocrinol, Jan 1 2004, 150:65-71, "Association of endogenous testosterone with blood pressure and left ventricular mass in men. The Tromso Study"
3) The Journal of Clinical Endocrinology & Metabolism, Feb 1 1997, 82(2):682-685, "Association between Plasma Total Testosterone and Cardiovascular Risk Factors
4) International Journal of Obesity and Related Metabolic Disorders : Journal of the International Association for the Study of Obesity, 1992, 16(12):991-997, "The effects of testosterone treatment on body composition and metabolism in middle-aged obese men"
5) Obes Res, 1995 Nov, 3 Suppl 4:609S-612S, "Testosterone and regional fat distribution"
6) Kidney and Blood Pressure Research, 2008, 31(2), "Testosterone and Blood Pressure Regulation"