Recursion is one of the strongest and most potentially game-breaking effects in the game (outside of its straightforward use-case of defending against specific times of "hate" from the encounter deck). Often, the power of cards is limited by the number of times you can play them-- most of the time, only three times per quest. Recursion lets you turn effects that would ordinarily be powerful escape hatches into reliable, repeatable tools.
What kind of attachments might be worth recurring with Second Breakfast? Many have noted the single-use (often free) attachments like Cram, Miruvor, or my favorite, Good Meal (all of which are a thematic home run with Second Breakfast). The payoff on these is lower, but they're quick, easy to set up, reliable, and cheap. Otherwise, player attachments typically stick on the character they're attached to (barring attachment hate from the quest), but anything that goes on encounter cards typically winds up discarded at some point-- Elf-stone, Ancient Mathom, Ranger Provisions, Thror's Map and Key, and many traps (such as Secret Vigil). And then there are the "single-use" framework-breakers-- Path of Need, Favor of the Valar, etc. If Second Breakfast is giving you an extra round without any heroes exhausting or an extra chance to survive threating out, it can easily be a game-saver.
But the most interesting attachments to recur with Second Breakfast, in my opinion, are the record attachments-- Scroll of Isildur, Map of Earnil, Book of Eldacar, and Tome of Atanatar. In this way, Second Breakfast can recur not just attachments, but also events (which are by their nature single-use and therefore better targets for recursion). And because of the way the record attachments work (recurring the event and then putting it back into your deck), each copy of Second Breakfast potentially gets you two extra plays.
In fact, because it is itself an event, it can be paired with Tome of Atanatar for infinite recursion. You blow up the Tome of Atanatar to recur the event of your choice, then play Second Breakfast to return the Tome of Atanatar to your hand. You blow up the Tome of Atanatar a second time to recur Second Breakfast, and for its target you choose the Tome of Atanatar you just discarded. Then you play the Tome of Atanatar again. It is now free to recur your preferred Leadership event again, and Second Breakfast is in your deck to repeat the loop once you dig it back out. (Easily done if your deck was empty when you started.)
This is an expensive way to recur an event-- with three Leadership heroes, it adds four extra resources for each time you loop your preferred event (though if you add a fourth leadership hero via Sword-thain, this falls to just two extra resource per loop). Each loop gets you two extra plays (once from the Tome, once from drawing it back out of your deck), so this amounts to two extra resources per play (one with Sword-thain).
But Leadership has plenty of events that fully justify the extra cost-- in multiplayer games, Grim Resolve, Strength of Arms, or Lure of Moria could easily ready 20+ characters at a time. (If you're using the pre-errata version of We Are Not Idle, looping that plus Lure of Moria could generate infinite resources, even accounting for the extra cost of playing each.) Sneak Attack + Gandalf is a bargain even at three resources per play since it preserves your Gandalf for future use. By the same token, Reinforcements is well worth the boosted cost if you have enough high-value allies in hand. (Though if you want to recur Reinforcements, there are easier ways to do so.)
The granddaddy of all game-breaking effects, though, is Doom Hangs Still, which completely shuts down staging for a round, albeit at a very high cost. But is any cost too high to justify the ability to prevent the encounter deck from revealing another card for the rest of the game?
So Second Breakfast really has three main use-cases: protecting against attachment hate, getting extra mileage out of single-use attachments, and insane recursion shenanigans. Any of those three can be enough to justify its presence in a deck. But my favorite part is how, once you're running it, everyone else at the table also benefits. Against quests with attachment hate, one player with Second Breakfast covers the whole table. If you're trying to recur Cram or Good Meal, everyone else gets to recur any single-use attachments they might have-- and even if they don't have any, they get a "free" discard to something like Daeron's Runes or forced discard treacheries, pitching an attachment (even one they want) knowing it'll soon be back in hand.
And finally, if you're using Second Breakfast for some game-breaking shenanigans, every other deck at the table is also free to get up to shenanigans of their own. The Tome of Atanatar + Second Breakfast combo only gives you infinite recursion for Leadership events. But once you're infinitely recurring a Leadership event, partner decks are free to run one of the other record attachments to infinitely recur events from different spheres, too-- say The Hammer-stroke and Thicket of Spears so enemies never attack for the rest of the game, or Advance Warning so enemies never engage for the rest of the game (ideally paired with Haldir of Lórien, Arrows from the Trees, or The Great Hunt to clear out the staging area), or The Galadhrim's Greeting so everyone's threat dial rolls backwards every round or Shadows Give Way so you never see another shadow card again. Because every sphere has a couple cards that just completely break the normal framework of the game, the potential for coordinated fellowships to just "turn off" whatever part of the game is giving them trouble is off the charts.
There's a reason why recursion effects are so rare, so limited, and so likely to eventually see an errata (see: Will of the West, Háma). There are few ways to more reliably break the game than getting extra plays out of cards that were balanced in part by the limited number of times one could play them.
