Slashgeo pointed me to a very interesting set of projects - SpatiaLite and VirtualShape. They provide a spatial data engine for the sqlite database. Think of it as the PostGIS of SQLite. It looks like this extends sqlite's spatial capabilities far beyond the sqlite OGR driver.
SpatiaLite provides many of the basic OGC Simple Features functions - transforming geometries between projections, spatial operations of bounding boxes, and some basic functions to disect, analyze and export geometries.
VirtualShape provides the really neat ability to access a shapefile using the SpatiaLite/SQlite interface without having to import a copy - it reads directly off the shapefile by exposing the shapefile and its attributes as a "virtual table". I can think of a million uses for this. For example, lets say you have a shapefile of US counties and the number of voter in the 2004 election as an attribute in the dbf. You want to find the total voter count in each state:
$ ls -1 counties.*
$ sqlite3 test.db
sqlite> .load 'SpatiaLite.so'
sqlite> .load 'VirtualShape.so'
sqlite> CREATE virtual table virtual_counties using VirtualShape(counties);
sqlite> select sum(voters) as total_voters, state_name
group by state_name
order by total_voters desc;
Now this is fairly straightforward non-spatial SQL but the ability to run it against a shapfile without having to export to an intermediate data format is a very valuable tool.
When to use SQlite.
A video presentation by Richard Hipp (the author of sqlite).