Does anyone know of a DBMS with global geospatial search?
The best open-source and free geospatial database is in my opinion PostGIS. It is easy to use and has a huge support group (also for example at  https://gis.stackexchange.com/)

It also connect to all sorts of different open-source programs and web-interfaces which should make data editing, viewing and sharing easy.

It can handle the date-line and the poles:

 4.2.3.2.
 What about the date-line and the poles?
 All the calculations have no conception of date-line or poles, the coordinates are spherical (longitude/latitude) so a shape that crosses the dateline is, from a calculation point of view, no different from any other shape. 


(http://postgis.net/docs/manual-1.5/ch04.html#id358535)

Link: http://postgis.net/