In general, you absolutley want to stay away from saccharin-based sweeteners which have been shown to cause cancer in animals (they often come in the pink sachets, e.g. at Starbucks). Nutrasweet (Aspartame; blue sachet) and Splenda (Sucralose; yellow sachet) based products are safe as far as I know (unless you have Phenylketonuria, a rare genetic disorder). However, they are only as safe as other artificial food additives (e.g., artificial colors, flavors, preservatives). That is, they are always not as good for your body as an all-natural diet would be.
I believe it's ok to use Nutrasweet and Splenda based sweeteners and diet soda products if you don't use them to excess (that is, make sure to also drink water and not just these sodas).
If you want to be absolutely safe, you should sweeten your coffee, tea, and desserts with Stevia, a calorie-free, sweet extract that's made from the Stevia leaf and is 100% natural. Stevia is available at health food stores. It's not cheap but will last you forever. In Japan, some diet sodas are actually sweetened with Stevia (e.g., Pocari Stevia), which would basically be the way to go.