Playing 2E in the Dallas area in the 90s, I played with a large community that used the battlemat in a specific way. Pickup games (at cons etc) used it the same way, if I recall correctly. From what I've read on some OSR blogs, groups in other areas didn't use battlemats or minis at all until 3.0.
When first sitting down to play, the battlemat would usually already be down, totally blank. Players tended to put their minis in front of them at the table. Everyone usually had a painstakingly painted mini. During setup and initial RPing, the DM might draw something out to help players visualize it occasionally, usually not to scale. The mat would be largely blank and minis unused until things turned hostile. All parts of the game before the first fight did not use minis at all unless a fight was likely.
When we had got to the first fight, or an RPing situation turned hostile, the DM would draw the area out on the mat and would dictate or negotiate where each character's mini was at the start of the conflict. Then movement, weapon/spell range, etc would come into play, and the mat/minis would be used. After the last creature was defeated, trap disarmed, or chest searched, the mat and minis would be largely ignored until the next conflict.
So, even trap disarming or searching weren't mapped unless related to a fight. Occasionally, it would be used in a situation that was only likely to cause a fight - sneaking past the Orc camp, for instance. Once in a while it would be used for long wilderness travel, to show the players the general area and track progress between random encounters. Of course, there were exceptions for situations where position was vital, but they were rare.
This method caused some interesting metagame tension. If the map came out, or if the DM drew an area to scale and had players place minis, you knew a situation was likely to turn hostile or a monster was around the corner. Players tried not to overtly let this metagame knowledge affect their character, but some would suddenly be more cautious or ask, "Do we hear anything?"
A clever DM would use it to their advantage - even if no fight was planned. If the players or characters were getting unfocused, bored, fighting with each other, or feeling directionless, it was a tool to bring focus back to the game. It said, this next part is important. This only worked if the majority of times there actually was a fight coming (or narrowly avoided), but when used judiciously, the players never knew. A DM could use it to create tension, and players would feel impossibly clever for having avoided a fight/explosion. (...or players spoiling for a fight would rush back in, banging pots together to attract the fight you thought you had avoided!)
In the 4E games I played after coming back into the hobby (and before discovering the OSR), the mat was used for everything. If something happened in-game at all, the battlemat was used. Peaceful interactions? On the mat. character intros? On the mat. I know this is likely unique to the groups I played with, as is the method above, but I found it very video-gamey - the mat was the virtual world, and everything happening to one's "avatar" had to happen on it, not in your imagination. (not edition warring here, relating my subjective unique butterfly feelings about a specific group. I know 4e can be used differently, and with the method above.)
So how did/do you use the minis, and battlemat?