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The Depot Agent who randomly shows up in the Big Stadium/Tennis Court and says he's lost. In B/W he was the only Depot Agent you could battle outside of the Battle Subway, then came the one in B2/W2 who replaced the Police Officer outside of Lostlorn Forest to seemingly advertise the Battle Subway. Their names are Josh and Hank, respectively.
Honorable mention to Ferris Wheel partner Rich Boy Martin. An entire month, without fail, I went to meet him every single day. I would wake up myself if I suddenly remembered in the middle of the night I didn't visit him that day and prompty battle him. I haven't battled him since the last day of that month. Sweet Martin, I'm so sorry. I wonder if he dies when B2/W2 takes place...