For me, this is a very scary question to even think about. I've been using FeedBurner since before they were acquired by Google and I've been pretty happy with it. But the question on many blogger's mind is will Google kill FeedBurner.
Matt McGee did a detailed write up on the signs on why he believes Google may indeed decide to no longer support and manage FeedBurner in the future. His reasons:
(1) They let the Japanese TLD of FeedBurner expire.
(2) FeedBurner's Blog & Twitter account were also recently shut down
(3) The FeedBurner support forums are dead and filled with spam
(4) It doesn't seem anyone at Google is putting any new features into FeedBurner
(5) Many people think RSS is dead and an old technology
For me, it isn't a huge deal. I use the FeedBurner MyBrand solution, so I control the domain and can switch it to my own RSS solution. But they do manage my email newsletter, which again, I can switch over to something custom or even switch back to FeedBlitz.
It is just a pain and I rather they keep it going.
What do you think?
Forum discussion at WebmasterWorld.