Are countered spells recycled or trashed?

When a spell is countered, it is placed in the trash, not recycled.

According to Rule 425.1.a, a countered spell does nothing and is cleared from the chain. Per Rule 156, spells are placed in the trash of the player who owns them after they create their game effect. Because a countered spell is not considered to have been played (Rule 425.1.b), it does not trigger any effects that would occur upon a successful play, nor is it subject to any "recycle" instructions associated with playing that spell (as detailed in RiftJudge FAQ #5621 and #8996).