Several artificial 'no' calorie sweeteners have been approved for use by national governmental bodies in various countries.  This post will not delve into their safety - I have done this on more than one occasion (you can search the blog) and have concluded for myself that the products are safe if used as intended.  (i.e. some are not heat stable and you should not bake with them) Regarding sensational stories associated with them, I refer you to which regularly debunks such myths.
And as I am known to say, if it turns out that these sweeteners do kill us - I will be dead twice.  
Of the products available for purchase, the most popular appear to be Nutrasweet (aspartame), Splenda (sucralose) and SweetnLow (saccharin).  I regularly use the first two, but not brand names.

So what is the worry with them?  Some research suggests that people who use artificial sweeteners or drink diet drinks actually gain weight.  Now don't panic.  First of all, the research is not the kind that can make a causal determination.  No study has ever said, diet soda's cause weight gain.  There are studies that show a correlation - or a coincidence - between diet soda consumption and increased BMI for one example.

I am not saying that people who use sweeteners won't gain weight.   I am saying that it is not because of the sweeteners themselves.  Some interesting research suggests two explanations for what is happening.  First, since we have all this fancy imaging equipment that we tend to over use, scientists have put people into  fMRI or PET scans to look at their brains after the subjects consumed sugar or an artificial sweetener.  Turns out - sugar taps into the reward center of the brain (yippee!) and sweeteners do not.  This means our bodies get different messages and respond in kind - you know different neurotransmitter action and all that.  Secondly, sugar has calories - empty as they are- sugar is still a source of energy.  Aspartame and the like do not have calories(energy).  Here is the key.  If you drink a diet soda or use a sweetener to cut back on say 100 calories, but you consume that 100 calories, and more later - then YOU WILL GAIN WEIGHT.  There are many reasons why we over consume and some of them happen by accident - we don't expect the meal at the restaurant to have 1200 calories - but either way - too many is too many and that's what happens.
If you can use sweeteners and regulate your intake - as I most certainly do - then this should not be a problem for you.

I suppose there is still more we have to learn about artificial sweeteners and I absolutely do not consider them a healthy product - but I hear sugar is itself toxic so- well - we have to limit it. 

** I am not making an endorsement, you must engage in your own informed decision making regarding the use of sweeteners.
** I will absolutely offer an opinion about the brands that fortify their products, you know with fiber and or vitamins.... THAT is NUTS - save you money.  Get your nutrition from FOOD - because that is where science says it works.  There is NO evidence to suggest that fiber in an artificial sweetener improves health the way it does in an orange or oat bran.