I'm glad someone has started this because was I was thinking of putting my recommendations up.
I will also mention Mike Duncan's The History of Rome it's probably the best out there.
In Our Time with Melvyn Bragg (and the archive podcast of this In Our Time Archive: History) from BBC Radio 4 availiable on iTunes and www.bbc.co.uk/podcasts
The History of England by David Crowther very enjoyable.
The China History Podcast by Laszio Montgomery He does not do a podcast from the founding of china to the present (probably because it's to long) but he does it on different topics each week.
The History of World War II Podcast by Ray Harris Jnr it's had 3 slightly different titles but this is the current one. He looks like he has put them all under this title now so downloading all the episodes should be fine. This is a very detailed podcast and is very good.
The History Extra Podcast (formaly the BBC History Magagazine podcast) by BBC History Magazine. It usually has 2 interviews related to the topics in the magazine.
These 2 are also well put together but i'm just not a big fan off them. These are:-
The British History Podcast by Jamie Jeffers
Russian Rulers History Podcast by Mark Schaluss
These are all usually on a weekly basis with the exception of The History of World War II Podcast but that is still regular. None of them neglect there podcast's and They are all worth trying at least once.