I have considered hosting myself, as I have some very nice 15mbps upload tubes that are rarely utilized. But that has so many issues, like Jlee says.
We are on a very nice shared server, whoever has the other slots does not have much traffic. To prove this, the server very rarely slows down for no reason, yet shows a very measurable decrease in speed (10% or so, not bad or anything) when we have hit high traffic patches. From this, I can deduce that we are the only site on our shared server that actually has any real traffic. Just guessing, nothing solid (I barely understand a lot of this stuff), but I would guess that one of our "neighbors", if you will, has hit a traffic spike, or is doing a big FTP transfer. Either way, ride it out.
Maybe someday, if we start making real money, we will rent or own a dedicated server, but that day is not now.