We have a need for this. My idea (which I came to post) was to have us be able to specify trending topics on the community overall (perhaps letting us choose which forums, so we don't have our Classifieds listings creating "noise"), and also trending topic per forum or sub-forum.
The flexibility would come from admin section which would let us specify exactly what we want in terms of trending. Perhaps base it on number of responses per day/week/specified amount of time, or do it on a percentage basis as it is more flexible than a hard limit. Add "likes" as a weighting, number of views, number of replies, etc., perhaps a dozen different criteria we can choose from.
Where it really can be powerful (and where we actually need this most) is as an RSS feed, so we can use this on a couple of our related WordPress sites, and also offer it to subscribers as a way to keep up with what's hot in the community.
This definitely should be core functionality--I don't trust some add-on developers here to be mindful of heavy server loads. After having our entire forum on a powerful server brought down by a single poorly-coded add-on with a poorly-written query, I would rather (in an ideal world) run the forum with no add-ons whatsoever.
