Vasectomies - some guys just can't wait for the day their wives say to "cut the ties" and other guys are very concerned. So who's right? Well, the bottom line is that so far there has been no convincing evidence that vasectomies put males, in general, at risk. However, there are some studies that will make you think.
But before we discuss those studies, I want to mention one thing: anything that gets you to have more sex will in general be healthy. See my pages Sex is Good for Your Testosterone and Sex is Good for Erectile Strength for some of the research showing this. And my point is that a vasectomy, for some couples anyway, can increase the chances of having sexual intercourse.
For males the reasons are probably 1) loss of concern about pregnancy and 2) being able to orgasm inside of the woman without a condom (assuming you have no concern about STD's), which is heaven on earth indeed. The most prominent reasons for females are undoubtedly 1) less need to use a condom so intercourse feels better and 2) less worry for the woman (or male) about pregnancy.
But, all of that said, I think a Vasectomy 101 might be in order here. Your doctor will probably not tell you any of this and it's good to be fully informed. (He or she often knows more about health insurance reimbursement than about the multitude of studies regarding vasectomies.)
First of all, one of the concerns about vasectomies was that they might somehow negatively affect male hormone levels. Most of us think, if you cut anything near my gonads, it's bound to negatively impact my testosterone. Interestingly enough, there are quite a few studies showing the opposite: a slight increase in testosterone. These post-vasectomy testosterone increases have shown up in various healthy populations.  And these slight increases in testosterone have even shown up in long term studies as well.  Of course, one could never advise getting a vasectomy to boost T, especially since some studies have shown no significant increase. (You may also be interested in my page on How to Increase Your Testosterone Naturally and Common Causes of Low Testosterone for more information.)
Another big concern has been vasectomies and prostate cancer, especially since some of the initial studies showed an increase in T. The National Cancer Institute has a valuable study  that every male should read before deciding on a vasectomy. This issue has been studied by teams of scientists with largely inconclusive results. For example, in March 1993, the National Institute of Child Health and Human Development (NICHD) held a conference and examined this issue. They found mixed study results and, furthermore, "could not find any convincing biological explanation for a link between vasectomy and an increased risk of prostate cancer". Similar large scale studies in 1997 and 1998 have found similar results. But be aware: there are a couple of studies that show a slight increase in prostate cancer risk 
Finally, there is the "dementia connection". There is a certain rather obscure form of dementia called Primary Progressive Aphasia (PPA), that ends up with the individuals having trouble remembering and understanding words. One researcher, Sandra Weintraub, first posited this potential connection. However, the contrasting argument is simply this: millions of vasectomies have been done through the world, especially in China, and there is simply not an army of men walking around with PPA. Again, though, it may be something to research if you are concerned.
One other side effect that doctors frequently do not inform their patients about is what's called congestive epididymitis. Basically, after a vasectomy, the sperm is trapped in the epididymitis where it is reabsorbed into the body. If sperm becomes "backed up", especially in (very lucky) men who have a lot of sex or produce a lot of sperm, scientists call this "congestive epididymitis" and it can cause some pain and discomfort to be sure. In fact, it can even rupture in some cases.
Here's my final shocker: some guys actually regrow the tube back together - yes, like a lizard's tail - and start pushing out sperm again. It is very unlikely, but is almost impossible to detect since it could happen in six months or in twenty years. Urologists call this "recanalization" or "spontaneous connection of the vasa defentia", which is medical name for the thing that your doctor took a big slice out of.
However, if those concerns all seem low risk and minor to you, especially compared to the benefits, you may want to go ahead. The procedure itself is relatively simple. Probably the most painful thing is the initial anasthetic, which is like a bee sting into the testicle area and usually repeated in the middle of the procedure. The post-operative pain is relatively minor, assuming you don't have to drive yourself home or have one of the kids welcome you home with a diving hug.
What might seem the worst part of it all for some guys is to go without sex for seven to ten days. However, that's just about the time that you feel like having sex, so that works out perfectly. (This is to avoid the "congestive epididymitis" mentioned above.) Most guys can even return to work after two to three days.
The decision is yours.
1) J of Urology, Dec 1995, 154(6):2065-2069
2) Intl J Andrology, 1987, 10:471-479
4) Br J Cancer, 1988 March, 57(3): 326 331, "Vasectomy, cigarette smoking, and age at first sexual intercourse as risk factors for prostate cancer in middle-aged men"
5) Fertil Steril, 1988 Feb, 49(2):309-15, "Annual variation in semen characteristics and plasma hormone levels in men undergoing vasectomy"
6) Fertil Steril, 1976 Feb, 27(2):144-51, "An investigation of plasma hormone levels before and after vasectomy"
7) Fertil Steril, 1975 Apr, 26(4):329-30, "Plasma testosterone, luteinizing hormone, and follicle-stimulating hormone after vasectomy"