Well, let me explain this briefly:
1.I want to build a website that provides location based services, like http://fireeagle.yahoo.net/ .
2.I guess most of these services have something do with longitude and latitude.
3.Is there any particular database/datastore/data structures fit well for such apps? I mean easy to store longitude, latitude and easy to compute or easy to use.
I am new to this and any feedbacks are welcome
Spatial extensions to relational database systems provide storage and indexed access the geography/geometry datatypes. They allow you to perform spatial joins and all sorts of spatial queries. In short, they are exactly what you need.
If you are using the open source stack I would recommend PostGIS, the spatial extension to Postgresql. If you are using the MS stack, try the spatial extensions to SQL Server 2008.
I would recommend you to consider GeoDjango
It is very nice, as it merges the simplicity of Python/Django and the power of PostGIS. But it can also be complex and provide too many features, therefore wasting your time.
If you don't have particular needs, there is another simpler solution to be used with Django or Python alone, that is Geopy. While not adding spatial extensions to a database, it allows you to perform Geospatial calculations using generic data structures (also any database). You can calculate distances, doing (reverse) Geocoding. Take a look at the Getting Started page, but also directly at the code, as it is well documented. I'm using it for a Dynamic Carpooling project and it works very well.
Both solutions fit well with the Django framework, so you coud easily develop a website around the services provided.