An entrepreneur with a great business concept or patent but little knowledge of how any of the technical details get implemented

I work closely with him or her to fill in all the missing pieces, educate him/her about all the options and potential risks and come up with a intelligent strategy for proceeding. If all goes well, a prototype might be built or perhaps even a fully functioning deployment is developed.

A newly formed business with an existing set of technologies that lacks overall cohesion, oversight, and/or proper management

Many businesses find themselves struggling with keeping their existing products or services up-to-date; either the original developer has left or is no longer able to provide adequate service or perhaps the right people weren't put in place at a crucial time.

An existing business wants to enter into a new market or explore a new technology

In this case I might take their functional specification (or help them write one first), then code it from the ground up.

Starting up a remote/virtual business.

In today's economy, more and more businesses are being grown remotely; it saves considerably on specific costs and often makes finding the right people easier due to the increased pool of available talent; however operating a remote business takes a considerable amount of skill and effort. Having a technical infrastructure and even more importantly a strong/expert management process in place is crucial for any successful business to thrive.