I added up the episodes and times from the Wikipedia list of Doctor Who episodes. This excludes movies and the 2013 50th anniversary docudrama as well as web episodes, animated features, etc.
Classic Who
694 episodes and 1 special over 26 seasons with a total run time of 295 hours. As noted in the comments, some of the early episodes are no longer available in video form.
Seas Year Eps Spec Mins
1 1963-4 42 1050
2 1964-5 39 975
3 1965-6 45 1125
4 1966-7 43 1075
5 1967-8 40 1000
6 1968-9 44 1100
7 1970 25 625
8 1971 25 625
9 1972 26 650
10 1972-3 26 650
11 1973-4 26 650
12 1974-5 20 500
13 1975-6 26 650
14 1976-7 26 650
15 1977-8 26 650
16 1978-9 26 650
17 1979-80 20 500
18 1980-1 28 700
19 1982 26 650
20 1983 22 1 640
21 1984 24 600
22 1985 13 585
23 1986 14 350
24 1987 14 350
25 1988-9 14 350
26 1989 14 350
1996 Made-for-TV movie
1 special with a run time of 89 minutes
Seas Year Eps Spec Mins
1996 1 89
New Who (through July 2019)
139 episodes and 16 specials over 11 seasons with a run time of 125.75 hours. The Wikipedia article includes most specials with the previous or following season. The exception is the 5 specials that were run between seasons 4 and 5 and the 2013 specials. I have followed the same pattern.
Seas Year Eps Spec Mins
1 2005 13 579
2 2005-6 13 1 645
3 2006-7 13 1 652
4 2007-8 13 1 690
2008-10 5 315
5 2010 13 625
6 2010-11 13 1 660
7 2011-13 14 1 710
2013 2 137
8 2014 12 586
9 2014-15 12 2 697
10 2016-17 12 2 681
11 2018-19 11 568
If you had access to all those episodes and wanted to watch them all, you would need 295 + 1.5 + 125.75 = 422.25 hours or nearly 18 days (if you could watch them non-stop).