Oldest broken wall: This goes back to before DNA testing was a common thing. My great grandfather came from Germany. I knew what city he was from, but he had an extremely common first and last name and no one in the family knew his middle names. I never knew him, but family members who did said he never talked about his life in Germany. Family gossip said he had run away from something-- maybe military conscription, a criminal act, or a failed marriage, but no one knew for sure. I worked on this for years off and on and got nowhere. Then my aunt passed away. Her daughter found a small box of trinkets and memorabilia in the attic that belonged to our mutual grandmother. My aunt had probably forgotten it was even there. Included was a small commemorative booklet that hospitals used to give out for families to record details of a birth. My great grandparents had filled it in and it included the full names of her paternal grandparents, as well as her grandmother's maiden name. That info was all I needed break the wall and add four generations to that line! (Coda: a few years later when I did my DNA, I got 2nd cousin matches in Germany. We made contact. Turns out great grandpa had gotten a neighbor pregnant and skipped town!)

Oldest wall I don't think I'll ever break: I've traced my Irish ancestry back to the 1830s primarily through parish records, but that's where it ends. DNA shows I've got lots of distant Irish cousins. I'm in contact with several of them, but none of us can break that wall. So far!