Topozone is a good source of USGS maps online.
Also, quite a few government agencies provide interactive maps from GIS data with ESRI's ArcIMS; some use MapInfo. Local government data tends to have higher precision and accuracy than state or federal because of the smaller areas covered-- it might be worth searching by county or city if you're interested in a particular area. One problem with IMS is that the interface is typically layed out like a GIS application, which is pretty difficult for most people to understand and use.
In any case, I think it's unlikely you'll find maps online that are very readable-- the best maps are custom-designed for the display size, view, and purpose. National Geographic does a good job customizing maps for screen viewing but they (at least the ones I've seen) aren't automatically generated, and they look good mainly because NG emphasizes background information like shaded relief, limiting detailed overlays like roads and labels. Interactive mapping software attempts to enable customization by size and view, but maps are just too complex and variable to customize using programmed rules and thresholds.
The main reason online maps look clunky, though, is that screen resolution is too coarse to display the detail a map is capable of portraying-- maps viewed on screen just can't match maps in print. IMO, the best you can hope for from an interactive map is a one that is useful for a reference but not necessarily easy or pleasant to read. Not to say Mapblast, Yahoo or MapQuest couldn't do a better display job with some tweeking and larger display space, but the medium itself is severely limited IMO.