If at a hotel, I never throw my outbound luggage tags away. I would always stuff them in the suitcase and wait to throw them away after all legs of that particular PNR/ticket were completed since, at least on DL, my name and PNR are on the luggage tags which is enough to login and at least mess with things. I also do the same with boarding passes though I usually keep those even after getting home and dump them in the shred bin at my office unless it's a BP I'm adding to the "Keep" collection box due it to being a special flight for whatever reason.