I don't think I watched any of my first animes to the end (Pokemon, Digimon, Dragonball, Inuyasha, Ranma and so on... )
Some, like Ranma, suddenly stopped being translated mid season and I didn't watch anything with subs at that time, others like Pokemon are rather endless.
If you seperate Dragonball into several parts (The first one, Z, Gt and so on), Dragonball would be the first (I didn't watch all of Z and dropped it when Boo appeared).
The first "real" completed one is probably Neon Genesis Evangelion.