The very notion of a mashup almost requires a good old tiled basemap service. The geographic reference is a valuable canvas of context to lob data onto. However, that context can sometimes prove overkill and the noise of what is essentially a reference map for driving directions clutters the thematic data overlain and muddles communication. Ideally you are working within the intersection of beneficial context and marginal noise, but that might not always be the case. So...
You may at times have a substantial enough set of thematic data, such that it inherently provides its own geographic reference, that it can stand on its own. In that case you might want to provide a "blank" basemap option, which nukes the cartographic basemap in exchange for a blank spatial canvas.
A thematic map of population migration in Southeast Michigan with a "Blank" basemap. Sometimes, if the overlain data is hefty enough to provide it's own geographic context, a cartographic basemap only adds noise.
That same thematic layer over Bing's hybrid map style. Hybrid can be attractive, and provide context, but sometimes there is too much secondary information and it detracts from the presentation.
Here it is with the road map style. The cartographic content provides some context, but again there is always a "noise" trade-off. Does the noise outweigh the context benefit? That's your call.
Here's how configure a blank basemap option in Visual Fusion...
<Basemap ID="Blank" Label="BLANK" MapBackground="#FFEFEFEF" GridColor="#80990000" Url=""/>
If you are bold and daring you can find more configuration doodads here.
Here is that same data, except rather than polygons (which can lead to larger, though not necessarily more important, areas demanding undue visual attention) we use dots. This is a fun case because the dots themselves are not as dense (and are closer to visual equals than their polygon treatment) but that dispersion causes them to suffer even more from the noise of a basemap. Here are some examples with various basemap options...
Cloudmade lets you create your own style of basemap; you pick what gets shown and how. In this case, I made a basemap style named "IDV Basic" which you can access, too, if you like.
But a blank, relatively dark, basemap isn't so bad either. The more I look at this the more I like it!
With a hybrid style, I can hardly differentiate my dots from the labeled elements in the basemap. Not perfect.
With the relatively light though very busy road style, I pretty much lose my thematic layer altogether.
In short, data is king. It will benefit from context, whether it comes in the form of additional feeds that buttress the data, cohort timelines or charts, or a helpful referential basemap. But don't let a busy basemap dictate the terms of your mashup!