So if/when I eventually switch to using a conical fermenter, I assume I wouldn't want to dump the entire trub/yeast cake at the bottom during fermentation. Do you typically wait until your "primary fermentation" period is over in the fermenter, and then dump all of the trub? If not, how much do you leave? How long do you wait before getting rid of some of the trub at the bottom? In most cases, would you completely avoid using a secondary and use the conical fermenter for the entire fermenting process?
Just like any fermentation process the best practice is to leave the beer on the yeast cake until it is completely done fermenting. And not just actively fermenting. Resting on the primary cake after terminal gravity has been reached for a few days goes a long way towards getting cleaner tasting beer.
I'd say do not dump until at least 10-14 days post pitching, assuming an appropriately sized pitch of healthy yeast was used.
If you're brewing an ale, I don't think there's any disadvantage to dumping the whole trub. If you were planning to pitch another batch onto it just drain it into a sanitary container. The trub is just inactive yeast and proteins. You'll most likely still have yeast floating around, and draining the trub will probably stir some inactive yeast back up into the beer. I'm not sure whether the same holds true for lagers.
I think most people wait until primary fermentation is over, although I'm sure there are some people who wait till the end and people who do it every few days.
The main concern would probably be how much air are you willing to let in the fermenter? Every time you drain trub or take samples it sucks in air (or, if you forget about your airlock, airlock liquid, hopefully not water). If you purge with CO2 it doesn't really matter, but if you don't you could possibly get some oxidation (although definitely no more than transferring to a secondary would give you).