I usually bill hourly, but sometimes as a day rate, almost always with a retainer that we bill against.
Typically, having a full-time CTO is the "ideal" situation. For a company who can't afford a full-time CTO, however, having a virtual CTO means that they get access wealth of experience that they'd otherwise never be able to afford. A startup who's business is based on technology in any meaningful way absolutely needs someone to fill that role—you can't (or shouldn't) just trust that a run-of-the-mill contractor is going to deliver what you think you're getting, and you probably aren't qualified to determine whether they are or not. This is the main reason outsourced projects end badly. Having a virtual CTO isn't as good as having a technical cofounder, but its a damn sight better than having no technical members on the team at all.
Typically, having a full-time CTO is the "ideal" situation. For a company who can't afford a full-time CTO, however, having a virtual CTO means that they get access wealth of experience that they'd otherwise never be able to afford. A startup who's business is based on technology in any meaningful way absolutely needs someone to fill that role—you can't (or shouldn't) just trust that a run-of-the-mill contractor is going to deliver what you think you're getting, and you probably aren't qualified to determine whether they are or not. This is the main reason outsourced projects end badly. Having a virtual CTO isn't as good as having a technical cofounder, but its a damn sight better than having no technical members on the team at all.