I've been doing a lot of computer quests lately, and my account has been filling up with cases.

I was just wondering if anyone knew whether or not the recycle beast ever asks for these, or if I ought to just delete them all...

Yes he asks for them, I remember he asked for the green case once. It's very rare and random but I know he'd ask for em.

Thanks so much for this answer

n_n

/siighs and throws them all in vault/