If you are talking about btrees, I wouldn't imagine that the additional overhead of a non clustered index (not counting stuff like full text search or other kind of string indexing) is even measurable, except for an extremely high volume high write scenario.
What kind of overhead are we actually talking about? Why would it be a bad idea to just index everything? Is this implementation specific? (in that case, I am mostly interested in answers around pg)
EDIT: To explain the reasoning behind this a bit more...
We are looking to specifically improve performance right now across the board, and one of the key things we are looking at is query performance. I have read the things mentioned here, that indexes will increase db size on disk and will slow down writes. The question came up today when one pair did some pre-emptive indexing on a new table, since we usually apply indexes in a more reactive way. Their arguement was that they weren't indexing string fields, and they weren't doing clustered indexes, so the negative impact of possibly redundant indexes should barely be measurable.
Now, I am far from an expert in such things, and those arguments made a lot of sense to me based on what I understand.
Now, I am sure there are other reasons, or I am misunderstanding something. I know a redundant index will have a negative effect, what I want to know is how bad it will be (because it seems negligible). The whole indexing every field thing is a worst case scenario, but I figured if people could tell me what that will do to my db, it will help me understand the concerns around being conservative with indexing, or just throwing them out there when it has a possibility of helping things.