Know of any C# spatial data libraries?

SharpMap is a (well known and used) OpenSource collection of spatial libraries for .NET

http://www.codeplex.com/SharpMap

Commercial libraries from ESRI would be the most widely used. Can I ask why you don't want to use SQL for creating spatial indexes?

http://msdn.microsoft.com/en-us/library/bb964712.aspx

If you don't want to create indexes in the database then you will be stuck using shapefiles:

http://mapserver.org/utilities/shptree.html

Update

I've not used NTS or JTS, but there is also a C++ implementation of JTS at http://trac.osgeo.org/geos/ which has an active user community, and I've used on a couple of projects.

Shapely http://gispython.org/shapely/manual.html builds on GEOS in Python. If you are doing everything in "the cloud" then it may be worth reading this article - http://sgillies.net/blog/986/manipulimization-of-whatchamacallems/

Re indexes - I found SQL Server + spatial indexes to outperform shapefile + indexes with the same data. If you require the indexes for displaying data then tile caches would perform far better than any indexing.

Python seems to have become one of the key languages in GIS. There is also an R-type index library - http://pypi.python.org/pypi/Rtree/

NTS is good...

Other stuff which may be useful now or later:-

GDAL/OGR for accessing different raster/vector formats PROJ4 for handling projections and transformations (Check out FWTOOLS download for the above in 1 install)

You should check out Mapwindow too... ver 6 is all re-written in .NET should be out soon if not out yet.. saw it at FOSS4G in Sydney.

http://www.mapwindow.org/

Of course PostGRES with PostGIS is a very powerful spatial database you can access from .NET

Also check out SQLLite which has spatial extensions for vector dat, and now RasterLite!!

Geoserver or Mapserver if you want to web enable anything.

Other general GIS apps to checkout: GRASS and SAGA

A Simple for QuadTree http://www.codeproject.com/KB/recipes/QuadTree.aspx