I dug up every artifact there was to find in the new Tomb Raider. I stepped on every antlion grub in Half-Life 2: Episode 2. I snagged every single feather in Assassin's Creed 2, and scrounged up all the rant-filled post-it notes Assassin's Creed Black Flag. Memory fragments, diary entries, special coins, silly glowing rocks: I've collected them all, and have loved basically every minute of it. Not because I think these things are of consequence - nobody actually needs 100 gold skulltula tokens - but because they give me a wonderful sense of accomplishment, and make me feel more connected to the world in which I found them.
That might seem like an odd thing to say, as the current wisdom is collectathons are an overdone nuisance at their absolute best. But where others see inherent awfulness, I see an issue of implementation, because good collectathons know how to make what they're putting down worthwhile enough for me to pick up. Take for instance the collectathon of collectathons, Banjo-Kazooie. Your task in this game is to collect 100 puzzle pieces called jiggies (10 in each of the nine worlds, and 10 more in the hub world) and a whopping 900 musical notes, all of which can be hidden just about anywhere (including, and this is true, in the u-bend of a giant toilet). The collection-averse probably shudder at the idea of that much gathering, but the thing about both jiggies and notes is that they serve a critical function for the game: you can only access new worlds by completing associated puzzles with the jiggies you collect, and notes open doors to each floor of the hub world so you can progress.
It's also not mandatory that you collect every single one of each, as you only need about 80% to make it to the final boss. Doing so, however, nets you special bonuses for the end fight, like extra projectiles and invincibility items. In opening up the bonus door, I felt an immense sense of victory even before I'd put downed my nemesis, and I knew every note I grabbed along the way got me a little closer to that goal. The joy of seeing my efforts bear fruit made the struggle and perseverance well worth it.
In addition, collectathons compel me to explore every corner of a game world, helping me learn about and feel connected to it in the process. While a game environment may be beautifully designed with a plethora of wonderful details, if there's nothing there for me to interact with, I probably won't bother straying from the beaten path. But scatter collectibles throughout that are worth finding, and I'll happily scrounge the four corners of that land searching for them, and end up seeing much more of what the game has to offer.
There's a caveat to all this though, in that the collectibles have to actually be relevant in order to get my attention. While I was happy collecting the post-it notes in AC: Black Flag (because they detailed the inner thoughts of a madman who was out to get me for reasons I didn't yet understand), getting the Animus fragments in that same game was an absolute slog, because they served no function except to exist. The only reward for tracking them all down is getting the numbers on either side of a backslash to match, so why bother?
Give me the audio diaries in BioShock, which help me piece together the rise and fall of Rapture and lead me to the places that suffered the most. Give me the lost memories in Alice: Madness Returns, that show what happened to Alice's family and what parts of her life determined the shape of Wonderland. Give me the thirteen songs in Ocarina of Time, which further my journey through the use of ancient, lore-coated magic. Overall, give me something meaningful that pushes me to explore the game, and lets me feel a sense of accomplishment when, many hours later, I finally ferret them all out. Do that, and I'll happily collect half-rotted bowls and tiny troll action figures. One down, ninety-nine to go - let the adventure begin.