If you use FeedBurner and you've logged in within the last couple of days, you've probably seen that your FeedBurner subscribers are at zero. Google is aware of the problem and is trying to fix it. As of this writing, I understand FeedBurner is still working, just not registering the count.
Still, this is a good time to download your email subscribers and keep the file in a safe place just so you have a copy of it. Because backing things up is always a good idea.
Here's how to download your FeedBurner email subscribers
Login to FeedBurner. You'll probably see that your subscriber count is zero. Don't panic. Just click on your blog name:
On the next screen, click on the "Publicize" tab:
Click on "Email Subscriptions" in the left column. Once you see a menu underneath, click on the "Subscription Management" link:
Next, scroll all the way down to the bottom of your screen. The number you see next to "Total Subscribers" is your email subscribers only, NOT your RSS subscribers (RSS subscribers aren't accessible). So, if you remember your subscriber numbers being much higher than what you see here, it's probably because you are used to logging in and seeing the total subscriber count (both RSS and email subs). Remember, this is only email subs.
Click on "View Subscriber Details" which should then give you the option to "Export CSV" underneath. Click on "Export CSV."
Once you download it, save this CSV file in a place you'll remember in case you need it later. For the time being, your emails should be sent out as usual. You probably realize this since you do subscribe to your own feed and haven't noticed it not being delivered, right?
I'm working on another post addressing the future of FeedBurner and what I'm reading. At this point, I don't think there's cause for panic. Look for that post early next week. Here's the post: FeedBurner Alternatives? What I'm Doing.
In the meantime, I think downloading your email subscribers is a great idea.