TL;DR: A bulleted list onlys show one kind of relationship (either sequence or membership in a set). If you want to show another kind of relationship, it's better to use something else. If you want to show sequence/membership AND something else, you can either use a different visual tool (not a list) or a list + additional dimensions.
Bullets are useful to help speakers remember what they wanted to talk about, but they're not a powerful way to visually convey ideas and relationships between ideas.
To quote Edward Tufte in The Cognitive Style of Powerpoint:
By leaving out the narrative between the points, the bullet outline
ignores and conceals the causal assumptions and analytic structure of the
He in turn quotes the Harvard Business Review:
Bullets leave critical relationships unspecified. Lists can communicate
only three logical relationships: sequence (first to last in time); priority (least to most important or vice versa); or simple membership in a set (these items relate to one another in some way, but the nature of that relationship remains unstated). And a list can show only one of those relationships at a time.
Bullets may be OK when you want to convey sequence or membership in a set. But even then, lists often have more than one dimension, in which case there are almost certainly better ways to present this than just as a plain text list with bullets. For example, take this slide showing an outline of a talk by Tom Rondeau:
and compare it to the classic way to show an outline with a list:
The point of this example is to show that the "plain" list, which is a fairly standard way to show an outline, conveys one dimension. The list version conveys sequence, which bullets can do fairly well (the parenthesis attempt to add another dimension, but it's subtle). The graphical version shows the sequence of the talk and also adds a color dimension to show the content of each section and its classification.
You could of course add extra dimensions to the list, too. This image was contributed by Eddie:
But if you are just listing points and not trying to show order, priority, or membership, all the more reason to stay away from lists.
Also see Bullets versus sentences in posters (I hate bullets in posters).