Yeah, Doctor Who's stories have always been serial in nature. I guess the main difference is that in the classic series they'd do four episodes for a particular storyline and then move on, whereas now it develops stories over the course of a season (or multiple seasons as the case may be). The good thing is that unlike most dramas nowadays, there are still plenty of standalone episodes that you can watch without having to have seen any previous episode.
"So Brak, is that Polish? Or... no I suppose it wouldn't be."
--Mike Nelson- MST3K: the Movie