No, there is not a maximum.
However, your mailbox can only hold 10 messages. The items you ordered will slowly roll in if you ordered more than 10.
For example, you ordered 16 items. The first 10 will arrive at the normal mailing time (assuming you aren't receiving any other mail). The last 6 will arrive at the next mailing time.
Yup, pretty much what Silently said. As for the HH Showcase, the maximum is five, if you are wondering about that as well, but most of us know since it tells you when you've ordered five.