Artificial sweeteners are incredibly popular and the reason is simple: they seem like a fantasy, almost too good to be true. Take the case of saccharin: it is about three hundred times as sweet as sugar and yet is zero calories. That's the allure: we get all the sweetness that we want with no metabolic or weight gain consequences.
Unfortunately, the picture is not so simple. Artificial sweeteners are not just a little artificial - they are very artifical and produce some very surprising (negative) effect, which we will cover below for each sweetener.
However, one thing that should be realized is that all artificial sweeteners will likely cause your problems and have been associated with obesity. In fact, one study found that regular consumers of artificial sweeteners, in this case saccharin, had their brain's reward system to sweets altered. Basically, regular consumers of diet beverages responded more strongly to sweets, thus making them more vulnerable to overconsumption and, eventually, weight gain. 
NEWS FLASH: One recent study found cancer-causing properties associated with aspartame and saccharin, two of the three sweeteners discussed below. 
Let's start with the three most popular on the market today:
This sweetener is almost synonymous with the word "diet" and is ubiquitous in diet drinks, including Diet Coke and Diet Pepsi. It is consumed in vast quantities by people around the globe and so it has to be safe, right? Unfortunately, nothing could be further from the truth.
If you haven't heard, aspartame is quickly metabolized by the body and broken down into some nasty chemicals, including methanol, formaldehyde and aspartate. The ensuing chemical soup is already linked to a variety of very serious conditions in both animal and human studies:
1. Excitotoxin Syndrome. This is a reversible but debilitating condition linked to the nasty excitotoxin, aspartate, that is metabolized from Aspartame. You can read more here in my link on Excitotoxin Syndrome. I don't know anyone who drinks more than, say, three Diet Cokes or Diet Pepsis that does not struggle with many of these symptoms.
2. Lymphoma and Leukemia. One animal study in a prestigious European journal already found "a statistically significant, dose-related increase in lymphomas and leukaemias in females" at about the equivalent level of three diet sodas per day.  This study was conducted on 1,800 rats and the control animals had no lymphomas. In contrast, the animals consuming aspartame had 10 malignant gliomas, 1 medulloblastoma and 1 malignant meningioma!
3. Kidney Decline. Kidney decline is nasty, serious business (likely from the formaldehyde metabolized from aspartame) has now been linked to this condition in a study of nurses.  Read more here at this link in the News Flash on the bottom of this page on Excitotoxins.
4. Testosterone and Reproduction. Numerous animal studies show that fetal excitotoxin exposure - excitotoxins pass rather easily through the placental barrier - can lead to reproductive and hormonal difficulties later in life. Read here about how Excitotoxins Can Decrease Testosterone. This may be an issue for us humans later in life, because cell phone and electrosmog exposure likely weaken our blood-brain barrier later in life. (Excitotoxins also go largely unimpeded into the hypothlamus where they can do considerable damage as well.)
Supposedly, the story of saccharin is like the story of death row inmates who are found later to be innocent and then freed upon the public at large. Many people, health conscious or not, know about how saccharin was implicated as a cause of bladder cancer in a famous rat studies of 1977-1980.  However, it didn't take long for several flaws in the study to come out, including the fact that fat metabolism is different and the dosage was much, much beyond any reasonable amount that could be consumed by a human.
Now the pendulum has swung back in the other direction and many consider saccharin the safest of the artificial sweeteners. I would argue caution for the following reason:
1. Liver Irritation and Toxicity. Saccharin can be hard on the liver  and is known for increasing aminotransferase levels, a sign of liver damage. One study on rats showed no liver cancer when saccharin alone was given to rats. However, when another liver-cancer causing agent was administred, saccharin greatly accelerated the rate of cancer.  In other words, saccharin may simply accelerate any underlying liver problems, a very serious problem indeed in our day of chemicals and drugs, which often overtax our livers. (In fairness, another similar study found no such toxicity. ) It should be noted, also, that one study showed DNA modifications from saccharin in mice. 
So far sucralose has avoided the spotlight as far as negative press and deservedly so: it has had, as far as I know, only one valid negative study to date: one set of researchers found that it negatively effected intestinal flora and pH.  If true, this is a very serious charge indeed as "gut flora", one's good intestinal bacteria, is critical for immune function and some digestive processes. Plus, the animals gained weight. However, more work is needed as this study has received some criticism for being insufficiently rigorous.
One last note: sucralose has been cited by Medscape as a possible migraine trigger in sensitive individuals:  This has not been verified, however, by a formal study nor do researchers know of any mechanism by which this might occur.
CAUTION: A lot of health-conscious people are running to Stevia and Agave as natural alternatives to sugar and alternative sweeteners. Yes, they are natural in the sense that they have been consumed as foods. The agave plant is grown in Mexico and is touted as a "low glycemic" sweetener. The problem is that it is relatively non-sweet in taste and, I just learned, very high (92%) in fructose.  In other words, it would be very easy to pack on the pounds with agave syrup. Furthermore, agave syrup does not contain fructose and the percentage goes up each year with increasingly modern manufacturing techniques that use higher and higher heat. One study on Stevia should give most guys pause: higher doses have led to decreases in testosterone and reduced sperm counts in laboratory animals. 
1) Eur J Oncol, 2005, (10)(2):00-00
2) Cancer Res, Mar 1980, 40:734-736 ,"Saccharin-induced hyperplasia of the Rat Urinary Bladder"
3) New Eng J of Med, July 14 1994, 331:134-135, "The Hepatotoxicity of Saccharin"
4) Envir Health Perspectives, 1983, 50:169-176, "Effect of DibutyInitrosamine and Saccharin on Glutamyl Transpeptidase-Positive Foci and Liver Cancer"
5) Toxicological Sciences, Received March 28, 1988; accepted July 12, 1988, 12(2): 346-357, "The Effect of Lifetime Sodium Saccharin Dosing on Mice Initiated with the Carcinogen 2=Acetylaminofluorere"
6) Boll Soc Ital Biol Sper, Dec 15 1980, 56(23):2486-2491, "Renal and hapatic toxicity studies in mice treated with sodium saccharin: breaks in single-stranded DNA"
7) J of Toxicology and Envir Health, Part A, Jan 2008, 71(21): 1415-1429, "Splenda Alters Gut Microflora and Increases Intestinal P-Blycoprotein and Cytochrome P-450 in Male Rats"
8) Drug and Chemical Toxicity, 2008, 31(4):447-457, "Genotoxicity Testing of Low-Calories Sweeteners: Aspartame, Aesulfame-K and Saccharin"
10) Journal of Ethnopharmacology, Nov 1999, 67(2):157-161, Received 30 November 1998;revised 22 December 1998;accepted 24 December 1998.Available online 10 September 1999., "Effects of chronic administration of Stevia rebaudiana on fertility in rats"
13) Physiology & Behavior, Available online 11 May 2012, "Altered processing of sweet taste in the brain of diet soda drinkers"