I was super fat years ago and cut out all sugar -- mainly full power sodas. I lost a lot of weight (obviously with other diet and lifestyle changes too) but was still a major diet soda drinker and would do a couple of cups of coffee or tea a day with a couple equals (aspartame) in them. I never had any ill effects that I noticed, but at some point I just felt like I shouldn't have that.
Back in April I decided to get rid of the aspartame too (well all artificial sweeteners). I'm drinking way more water now. Haven't had a single soda, and do drink a bit of fruit juice (really hard to find pure non HFCS adulterated fruit juices). For my coffe/tea I switched to Truvia which is a mix of stevia extract and an extract from grape leaves and stems. It's nowhere near as sweet as sugar or the artificial sweeteners, but you get used to it, AND it's natural.
I have to say, I don't feel any different that I know of, but with all that artificial stuff (I also ditched preservatives, colors, and flavors just to see if I could), I have noticed my food tastes WAY better.
If it weren't for the fact that I don't want to screw up my "hey I haven't had this in..." deal, I am tempted to drink a diet soda or use some aspartame just to see if I feel funny. Who knows.