While not from another game, but something I've used on and off in my 5E house rules is the 3d20 system:
You use the middle roll of the three d20s. Your average is still 10.5 and the variance is lower than just using a d20.
You use the highest of the three d20s. Your average is 15.49, almost exactly 5 points better, and your variance lower.
You use the highest of the three d20s. Your average is 5.51, almost exactly 5 points better, and your variance lower.
Why do I like it? For a few reasons:
1. By using the d20, you don't have to change any numbers.
2. While not a "bell curve", it is centralized more around the mean, making the typical result more common and the extremes less likely.
3. Having advantage (or disadvantage) shifts the average +5 (or -5) points. This makes DCs effectively shift one place, making a Hard task Moderate (or a Hard task Very Hard). It also mirrors the 5-point adjust applied to passive scores.
Critical Damage, Not Critical Hits
For a long time now, my group has replaced critical hits with critical (i.e. exploding) damage rolls. So, this means the result of the attack roll does not determine the chance of criticals.
OPTIONAL: Something new we have been exploring is making a "Critical Hit" when you hit by 10 or more, but I don't know if we'll do it or not. We are keeping critical damage, regardless.