I'm in this for the science, so I cap one and immediately open it. That's too soon. I then chill one at four days to drink on the fifth. Still, too soon. At seven days, I've had quite drinkable results. There are people that advocate a two to thee week conditioning time. Those people aren't drinking my beer though.
Based on a lot of impatients and testing. My results are thus. Take them with a grain of beer. I mean, salt.
Pretty much less than 7 days, and it isn't likely you'll be carbed all the way. Less than 5 days and generally it just isn't good. Oh, that doesn't mean it stinks, just that the level of carbonation and some residual sugars aren't where it should be.
I find that fully carbed hits between about 7-10 days for most typical beers, but then probably need a couple of days in the fridge to get it all absorbed up. Bigger beers, like a RIS or barley wine can take 2-4 weeks to fully carb because the yeast is really slow most of the time.
That said, I find most beers improve with a few weeks in the bottle, even if they have reached perfectly carbed status. Depends on the style, gravity, etc. I've had beers that were roughly at their peak at a month (most IPAs), 2 weeks in the fermentor, 2 weeks in the bottle. Peak beer. Throw it all in the fridge and start drinking. I've had RIS and barley wines that hit their peak at 3-4 years, which doesn't mean they weren't good before then.
I generally stick with "sampling" the batch starting at 7 days post bottling. Just making sure that nothing has "gone immediately wrong" during bottling. Also to get a better feeling for what the beer is like carbed up. I tend to just drink a bottle a week of the new batch until I hit about 3-4 weeks post bottling. Then I'll tear in to it.
Tearing is relative though as I usually have 5-7 different beers in the bottle at once.