I prefer downtime activities to be announced after the gaming session, when it's obvious the character will have downtime and we take this opportunity to call the session off. The players are still with their creativity to the max and can throw wild ideas. As the GM, it allow me to pick up some ideas and sort them into three categories: non-interesting activities -- not uninteresting per se, but for which I can't see something interesting evolving from at the moment (and these would be abstracted away with a few dice rolls like the "run your own business" rules), interesting activities (that can be integrated into the next session to whet the appetites if I can see some scenes being interesting to play at the beginning of the next adventure -- and for those, I try to have a nod to these activities in the next adventure as the players declared they were interested into this aspect of their character and full-on adventure seed, because in some cases, players throw useful ideas that need to be picked up. Once, they wanted to research information on a (undevelopped) NPC who they felt wronged them, so this NPC marchant was promoted to big villain status sometime down the way. Having the players choose at the end of the session (or right after, through emails) allows me to prepare interesting complication of the second-tier idea and work the first-tier ideas into the adventures. I'd be less likely to do that if I just learnt they wanted to build a castle (spanning many ideas), but they just tell me before the start of play... (I guess I am bad at totally freeform play).
How much depends on the campaign. I prefer episodic campaign where the heroes can lead "normal lives" between adventures, so it's usually every few game session that they can have extended downtime.
