Read, or maybe skim, this article. It's long but really interesting.
I"ll give you the lowdown:
A very large meta-analysis was published about the impact of artificial sweeteners on bodyweight.
Early media attention was highly inflammatory, with headlines like, "Consuming food and drink containing artificial sweeteners could lead to weight gain and heighten risk of suffering from health issues including diabetes…"
Actually carefully reading the paper indicated not only that the paper did NOT show what that headline said it showed, but that, in fact, in most of the studies, those who consumed artificial sweeteners lost as much or more weight than those in control groups.
Additionally, some of the studies were looking at artificial sweeteners in ways that nobody cares about. For example, one study had test subjects taking stevia in a pill. Do you care if stevia pills will help you lose weight (well, you might if it worked). No! You (we) want to know if drinking sweetened beverages in place of sugar containing beverages will help us lose weight. We want to know if Diet Coke will kill us or not (well, I care about Pepsi Max, because that is my favorite soda in the world, but Diet Coke is the more famous example.)
You might be the sort of person who is bombarded with scare articles and facebook posts about how aspartame causes cancer and all sorts of other nonsense. Let me sum it all up for you.
If any artificial sweeteners were VERY BAD, the way smoking cigarettes, for example, is VERY BAD, we'd know. Tons of studies have been done, and rarely do they show much of any negative health impact for pretty much any artificial sweeteners on the market. Even saccharin was only dangerous when fed to mice in truly ridiculous doses (it was the equivalent of a human taking 1,000 packets a day of saccharin, which nobody was doing).
Is water better for you than Diet Coke? Common sense says: Probably yes! But how bad for you is Diet Coke ? Common sense says: Probably only a little bit, at most!
So you have to slip into the second order question: how much do you enjoy your diet soda? If consuming some diet soda is a cornerstone of your happiness, you're probably better off drinking some. If you can take it or leave it, you're better off leaving it.
I personally have tried to cut back on my diet soda consumption. But I'll tell you, when I'm having a difficult time in life and I'm slipping towards food-binging behavior, I'll often circumvent the binges by pounding back a liter of Pepsi Max.
Is drinking a liter of Pepsi Max good for me? Probably not. But is it better than eating an entire pizza by myself, or a pint of Ben & Jerries? Almost certainly yes.
Diet soda is slightly bad for you. If it were very bad, we'd have people dropping dead left and right of aspartame related illnesses (the stuff has been widely used for over 30 years). That just isn't happening.
When confronted with things that are slightly bad, you have to make smart decisions - how much energy/ willpower/ suffering will it take to cut this thing out of your life? How much willpower/ mental energy do you have to spare?
And if you're interested in some careful analysis of published research, and a careful consideration of the methodology involved, read the article at the top of this post. It's very well done.