There are various software packages available on the open source market that will allow you to publish GIS data on the Internet.
Most of these packages are compatible with an array of GIS data formats such as ESRI Shapefiles, MapInfo Tab and opensource layers such as PostGIS and MYGIS layers.
Illustration 1, shows PostGIS data publish on the net directly out of an open source data warehouse facility. This solution consists of two components one which is the Geo-Database and the other a server that publishes the data to the Internet.
A typical solution will constitute of the following:
1 x Server
1 x Geo-Database
1 x GIS Data Publisher
1 x Web Browser/Viewer
Cost of a solution depends on the components used, but we are talking about open source so the above mentioned is totally free.