There has never been on-screen complete nudity in Doctor Who, though there has occasionally been implied nudity off-screen played for laughs. The Third Doctor is seen taking a shower in "Spearhead from Space" and the Eighth Doctor appeared with just a thin sheet covering him and the Tenth Doctor's clone was naked when he generated a body to go with his hand in "Journey's End". The Eleventh Doctor was also nude while changing from his raggedy suit as Amy Pond watched him in 'The Elevanth Hour'. He was also seen in the shower, whilst being a lodger in "The Lodger". The Eleventh Doctor was also painted naked, and shown (implied) naked under a girl's dress in "The Impossible Astronaut".
There has occasionally been minor nudity on-screen in Torchwood, an adult-oriented series which takes place in the same "continuity" as Doctor Who
Don't forget Sergent Benton in "The Time Monster".
Probably not what you meant, but it's a well-known fact that the Tenth Doctor had sex with Elizabeth the First.
Also when jumping through cars in "Gridlock", the Doctor meets a pair who are naked and cover themselves with newspapers.