First one you may know already or have at least always wanted to learn.
Sahanaavavatu Peace Chant Tutorial- Srivatsa Ramaswami
This is one of my favourites
Trayambakam ( Mrityunjaya mantra) chant Tutorial-Srivatsa Ramiswami
Another favourites but this one is tricky.
I'm sure Ramaswami must have winced once or twice as we were learning this on his TT course at LMU in 2010. It was OK while he was going through it word by word, phrase by phrase but we would go back over all the chants we'd been working on and some of them were more of a a struggle than others, this one in particular. The funny part was that there is a last phrase that gets repeated throughout and whenever the class would get to that bit after stumbling through the first part we would all sing out strong and loud.
I needed more work on this and thankfully Josh has posted a recording of Ramaswami working through the mantra on the 2012 TT.
And here's the tutorial from Josh Geidel