The most commonly cited moment for feels in anime is the end of Clannad: After Story. Pretty strong stuff but you need to watch the full 48+ I think eps to get to that point, and of course skipping the rest would just ruin the effect.
Something similar: It's said Aria the Origination (the final season of Aria) is the best one, so some people actually don't bother with the rest and just watch "Aria the Origination" and expect themselves to get something out of it. However, the point is, it's so good because it's the endpoint of all the characters journeys. You have to have been there from the start for anything to make sense or affect you. The core concept is about the cycle of life through apprenticeship, journeyman and master, and about going with the flow of life. Skipping to the end is just dumb. Just don't bother starting Origination if you're not interested to see the whole thing, it's the exact opposite of what the entire show is about: the show makes a big point of how much people are missing when they're in a hurry to get somewhere, so it's highly ironic that a bunch of people want to watch it because they've read the rave reviews, but they're looking for some magic fast-forward button to get through all the "slow bits". Hint: it's all slow bits, that's what the reviews are about.