Google Maps' tiling has become a de-facto standard for Internet maps. You can see how it works in this interactive demo. Basically every map tile is named by three numbers: the zoom level and an X,Y coordinate. For example, most of San Francisco is contained in tile z=11 327,791. Oregon is in z=5 5,11. Google, Bing, and many open source tiles use the same tile cuts, albeit with different names. The maps are based on the spherical mercator projection EPSG:3857.
How big are the tiles, what scale is the map? The best explanation I've seen is Microsoft's. Tiles are 256x256 pixels (by convention). At Z=0 a single tile covers the whole earth (except the poles). Each progressive zoom level is 1/2 the scale. Tiles are always square, but get smaller the further you are from the equator. Tiles "naturally" get less wide (in meters) because the lines of longitude narrow at the poles. The conformal projection we use for tiles also causes the tiles to get less tall (in meters) so that each tile remains square. I'd love to see a 3d globe with this tile mesh draped on it!
Here's a table of map scales for various zoom levels, see also my spreadsheet. "Feature" describes something that will generally fit in a single 256x256 tile. "One pixel" is miles or feet per pixel. All values are calculated at 37N, the latitude of San Francisco. Tiles at the equator are roughly 20% bigger on a side than in San Francisco; at 60N they are roughly 40% smaller.
I'm particularly interested in elevation and terrain tiles. SRTM has global coverage at roughly 90m or z=11. NED 1/3 is US coverage at roughly 10m or z=14. Google's terrain layer provides tiles globally to z=15, but it looks pretty averaged in remote locations.
Caveat: I've found a lot of conflicting tables and explanations of map tile scales: it may be I've got something wrong. See also OSM and this discussion. I also ran into an interesting spreadsheet, the time and storage requirements for a tileset (from Geosolutions). The globe to z=12 takes about 3 gigs of disk and a day to render.
See also rules of thumb for geocoordinates