Hi!
As far as I know, not requesting anything is a special event, as you then don't make a trade agreement with the civ. Basically, though, I suggest making such agreements as it can help make a lot of profit (if they are willing to pay 190% for legwear next year, you can be sure I will be making leggings for major profit).
Requesting a lot of different things will cause just a little of each to be brought, and it is in general not really efficient. The best situation is requesting just a few things you really need and leave the rest to the caravan. Then, they will not increase the prize for goods (for instance, I buy all cut gems I can get, but I never request any. I just hope the caravan brings them, as they are not essential).
Finally, I have observed that besides the requesting of items, decorations can alter what a civilization offers for an item. So, with a decorated item, always 'v'iew it before trading. I had some items where the elves with whom I don't have trade agreements offered me nearly twice the normal value because of some image of larches on them. At other times, I had an item worth 580, but the dwarves offered only 360. I suppose they didn't like the decoration.
In general, trade agreements are good for getting things you really need (wood, colored stone, certain ores come to mind) and the caravan's request are the best way to get enough trade goods ready with the least effort. So, I can only recommend that you try to get some agreements going each year (if nothing else, ask for wood or some other cheap items).
Deathworks