Many years ago, cyclamates were the first to be used in diet coke, but it was banned when cancer was found in lab rats consuming the cyclamates. They switched to saccharin and that was banned for about 14 years, but by then diet coke and others started using aspartame. Today there is a great suspicion surrounding the safety of aspartame, to the point that I'm nervous as well. They do have only Splenda diet coke and also Splenda plus acesulfame-k diet coke (I'm not happy with that last sweetener). Since my family has consumed Splenda (sucralose) for many, many years and in quantities most people would not have, I'm more comfortable with it. I'm not saying I know sucralose to be perfectly safe, only that we've not experienced any noticeable ill effects.
As I mentioned before, I do drink diet coke, but have cut down and have it mainly at restaurants when I feel like it, but typically I drink water or use a packet of Splenda-sweetened herbal tea in it. It might interest people to know that a diet coke is coming out using Stevia - possibly by the end of the year depending on FDA approval. This would be interesting to try for sure. I believe it is in a form of Stevia called Rebiana, a more pure form of Stevia without the licorice aftertaste.