I would like to know if there are online brokers that allow for an API
interface for trading, and if so, which "languages" APIs are available
in, and what are the cheapest services.  Constraints would be: must be
able to trade stocks AND mutual funds, and would like to be able to do
electronic fund transfers programmatically as well.

I know a guy who lost an awful lot of money doing this.

Heheh, I can imagine. I don't have any wild get rich schemes in mind.
I just spend too much time repeating things that are automatable..

I'm not sure what exactly may be out there, but I am sure there is
something by now. If nothing else you may be able to do something from
scatch by figuring out what format of HTTP commands are sent to their
servers and just do that programatically, with your favorite
programming language. However, an API would be much preferred. I
imagine such newly-developed interface would involve XML nowadays. Big
trading houses have had technical interfaces to automatically execute
trades for a couple decades now. In fact, I've read that such
computer-executed "program trading" had alot to do with the 87 "Black
Monday" stock market crash. The problem was that everone had the same
or similar programs.

You should check out Tradestation at www.tradestation.com.  They are a
direct access broker that allows you to write custom programs that
interface with their platform.  They use a product called Easy
Language which is very similiar to VB.  Plus it is one of the few
brokers that allow you to back test you ideas.  Hope this helps.