Far too many memorable moments, and here are my top ones for Series One (Season 27). Every Doctor Who fan has a moment that started them on the road to obsession. In my case it seems to be the entire of this series.
No episode of this series seems to be anything less than 'good' (Boomtown being the weakest of them).
Stand out moments:
In Rose: The first appearence of the Doctor
'What's your name?'
'Rose'
'Nice to meet you Rose! RUN!'
In Dalek: The first appearence of the Dalek and the first words:
'EXTERMINATE! EXTERMINATE! YOU ARE THE DOCTOR! YOU ARE THE ENEMY OF THE DALEKS! YOU WILL BE DESTROYED!'
The Entire 'Empty Child:The Doctor Dances' serial. Would work equally well in either episodic format or a UKTV Gold-style movie format. Likely to be immortalised as one of the top 10% of all stories in future years.
In Bad Wolf: Big Brother housemates being transmatted aboard the Dalek spaceships

probably to be exterminated or mutated into Daleks.
In The Parting of the Ways: the Emperor Dalek, the 'Loads of Daleks' scenes, Rose Tyler as the 'big bad wolf' not to mention the regeneration of the Ninth Doctor into the Tenth.