Since a plant isn't born the day one takes ownership (unless sprouting seeds,) this is actually 2 separate questions, "Which plant have you had the longest," and, "Which of your plants do you think is the oldest?"
To answer the former, I've had plain green Chinese evergreen, heart-leaf Philodendron vine, and plain green spider plant since the early 80's. They originally lived in a planter together. I've added many pics to the DB entries here:
Chinese Evergreen (Aglaonema modestum)
Heart Leaf Philodendron (Philodendron hederaceum var. oxycardium)
(I don't keep this in a pot anymore, the love affair is over:)
Spider Plant (Chlorophytum comosum)
It's impossible to say for sure, but I don't think those are the oldest plants that now live @ my house. About 20 yrs ago, my Gramma gave me a Dracaena marginata tree and a pot of Sansevieria that she'd had for many decades (and were of significant size when she got them.) So both of those are at least 80 yrs old, though certainly none of the individual leaves are that age.
Dragon Tree (Dracaena reflexa var. angustifolia 'Tricolor')
Snake Plant (Dracaena trifasciata)