The problem lies in being able to present a collection of items to a user in such a way as not to force favouritism on any one item other than by the order in which they are sorted.
A table is usually the best way of doing this because it naturally provides identical horizontal or vertical spacing to an item allowing the eye to easily scan rows and columns to view the contents without having to work hard to assess the content in a slightly different way when moving from one item to the next.
So why would you not use a table? Well - you might want to do more than just present the data in a 1 or 2 dimensional format - for example you want to add another dimension in which items are in some way sorted.
If you're going to add another dimension, you might think of using changes in appearance or types of markup for items but that adds to the clutter and reduces ease of visual processing, so position and alignment (and other gestalt principles) come into play - for example you present hierarchical or grouping information by indentation or whitespace, or even clustering.
But whatever you do in this case it has to be in context, for good reason, and must present an efficient and easily digestible presentation of content both from the aspect of overview or on detailed examination. It should present information in the user's mental model - not just because you happen to have that particular structure of information in the system model.
And that's why 'it depends' - since departing from the visual processing efficiency of a table, and the directions that you go in are really going to be driven by the data and context.
JohnGB mentions tag clouds in which the size of the item provides the sorted dimension, but (as he indicates) really tag clouds are only useful for short terms without additional data displayed - and they are only a marginally useful format at that (the only benefit is proportional representation) - so more of a fun or interesting format than actually being more efficient.
Since you seem to be talking about products, categories, users - I wouldn't consider much beyond incorporating groups and whitespace into your tables, but as I say it depends on your data and what you want to present to the user. If your showing users, you might want to indicate geographical location (via a map underlay) for another dimension...