Season 1: 1963-1964-William Hartnell
Season 2: 1964-1965-William Hartnell
Season 3: 1965-1966-W Hartnell
Season 4: 1966-1967-Hartnell/Troughton
Season 5: 1967-1968-Troughton
Season 6: 1968-1969-Patrick Troughton
Season 7: 1970-Jon Pertwee
Season 8: 1971-Jon Pertwee
Season 9: 1972-Jon Pertwee
Season 10: 1972-1973-Jon Pertwee
Season 11: 1973-1974-Jon Pertwee
Season 12: 1974-1975-Tom Baker
Season 13: 1975-1976-Tom Baker
Season 14: 1976-1977-Tom Baker
Season 15: 1977-1978-Tom Baker
Season 16: 1978-1979-Tom Baker
Season 17: 1979-1980-Tom Baker
Season 18: 1980-1981-Tom Baker
Season 19: 1982-Peter Davison
Season 20: 1983-Davison
Season 21: 1984-Davison/Colin Baker
Season 22: 1985-Colin Baker
Season 23: 1986-Colin Baker
Season 24: 1987-Sylvestor Mccoy
Season 25: 1988-1989-Mccoy
Season 26: 1989- Mccoy
New
Series 1-2005 Eccleston
Series 2-2006 Tennant
Series 3-2007 Tennant
Series 4 and Specials 2008-2010-Tennant
Series 5-7-2010-2013-Smith
Series 8-2014
The classic series (1963-1989) had 29 series. The revived series (2005-present) starts its eighth series this year. That's 37 series; it also has a 1993 TV special (Dimensions in Time), a 1996 TV movie, various 1999 parodies (most famously The Curse of Fatal Death), various webcasts (2002-2004 if I recall), two animated specials (2008 or 2009 if I recall; The Infinite Quest, Dreamland), plus two 60s movies based on it. Which is quite a lot of Doctor Who!
Season / Series 34 / 8
starring Peter Capaldi as the Doctor.
Thirty-Three in all. The Thirty-fourth series starring Peter Capaldi as the twelfth Doctor is being filmed now and will be broadcast later this year.
7 series of the revamp(8th is being filmed now), 26 of the classic series parts of which are missing so unavailable to watch though no full series is missing