Disclaimer: I've only watched from the start of Christopher Eccleston's tenure to about halfway through Matt Smith's tenure (think the final series I bothered watching was the 6th, where things started getting horrible).
My favourite episode, by a country mile, would be "The Girl in the Fireplace". Hits a great emotional note; has a fantastic sci fi/historical setting melded into one and is just an all-round fantastic example of what the show could me. And made me a massive fan of Stephen Moffatt after that.
It's a shame he couldn't keep that level of quality up as showrunner.