How to estimate or approximate a 3-D surface

Locfit has worked well for me.
http://cm.bell-labs.com/cm/ms/departments/sia/project/locfit/

Unfortunately it has not been updated for current versions of R: it also 
writes diagnostic output to stderr which is not shown on GUI versions of R
(especially on Windows).  There is a version in the Devel area on CRAN.

Package akima is the most obvious choice for interpolation.  For
smoothing, there are all the various spatial packages (and package fields)
as well as mgcv and gss already mentioned.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595