Luke Wrobleski has written a great article discussing the difference between perceived and actual simplicity and what it means to designers. Simplicity is more than the perception of spareness or bareness of design. In actuality, simplicity probably has more to do with ease of use than with appearance, and achieving simplicity can be a complex task.
Wrobleski illustrates the Pareto principle applied to expert user features on sites like eBay and You Tube. On those sites 80% of activity comes from perhaps 20% of the users. These are often the expert users, who want to do more than simply find products or watch an occassional movie. Those users are the one's that add the most value to the system, so features that enable those users to be empowered need to be addressed. So how does that user type's need impact simplicity of the experience for others?
Tufte speaks of information density, how much screen real estate is devoted to useful information, as a measure of an information object's effectiveness at communicating messages. "Usefulness" is the operative word there. Data dense interfaces don't necessarily lead to ease of use. The point is that if the ratio of useful data to chart junk is good, the object has better information density. It is the usefulness of the interface for helping users get things done is what leads to actual simplicity.
Achieving a simple experience when the spectrum of needs of users are varied is complicated, but possible. He points out that some interfaces have tried to balance those needs, e.g. Microsoft Office's partially hidden menus. I don't know many people that would argue that the MS menu design has lead to a simplified experience.
The implication is that you probably want to find a way to make expert-enabling features available because they probably serve that 80% of value to your product or service. Making those features available is what makes the experience simple for those users. But how to do it? One suggestion in the comments is practical and probably generizable for most web sites. Michael Zuschlag writes:
I think the answer is that, while experts do use expert features, even they rarely use them. Most of the time expert features are a distraction even for experts. That doesn’t necessarily mean designers must eliminate or hide expert features, but it does suggest that designs should be proportional, with commonly used features easy to see and select, and rarely used expert features being less obtrusive, even if less convenient.
Sound simple enough? The proof, I suppose, is when the executed design is deemed useful to the types of users it serves.