Nice question.
There are several ways how to get these information.
http://www.fallingrain.com/ : free to use, no registration needed.
World database of the airports and waypoints.
From these information you could easily make DB for waypoints.
EUROCONTROL
EAD ( https://www.ead.eurocontrol.int/eadcms/eadsite/index.php.html ): free to use, registration needed.
Big advantage - real and up to date information for all ECTL countries.
But a bit difficult navigation.
JeppView ( http://ww1.jeppesen.com/ ): very expensive SW, but the best in this time.
You will find there all information which pilot needs.
But it is not real database.
Garmin for pilots ( http://www.garmin.com/en-US/explore/intheair/ ):
another not free SW, very similair to JeppView but lightweighted. NAVIGRAPH ( http://www.navigraph.com ):
Great DB of all things which you need in FMC.
But I guess that they have it just for flight simulator.
OpenFlights ( http://openflights.org/data.html ): free DB of airports, airlines and routes.
You could downlod all data in one file :-)
aviation.stackexchange.com/users/4110/astrak
I use the National Flight Data Center at http://nfdc.faa.gov
I had to write them a letter explaining why I wanted the data ( http://fplan.sf.net ) and
they provided me with a login.
Now, every 56 days, they send me an email telling me there's an update available.
Bad news: they recently switched from a flat file to some unbelievably convoluted xml format that I haven't yet written a parser for.
Also, it comes with a disclaimer that the data is not approved for navigation.
Given that I've already found two minor errors in it, just in the SF Bay area, that's understandable.
Edit: I forgot to mention that I keep a subset of the data on-line at SourceForge.
I try to keep it up to date.
It's at the Fplan project .
These files are in the old "nav" format; documentation is included in the zip file.
If someone needs these files, they're freely available and I'm happy to make small additions to the data if anybody wants, since I already have the tools to parse the FAA data files.
I'm also happy to share the tools if anybody wants.
aviation.stackexchange.com/users/87/Edward Falk
Another good one for airports and navaids: http://opennav.com/ - has VORs, waypoints, etc.
aviation.stackexchange.com/users/20443/TheStoryCoder
I have successfully used The GPX Aviation Waypoint Generator from the free Navaid database ( http://navaid.com/GPX/ ) that outputs a GPX (XML type) file with all the waypoints, airports and every other elements you choose to include.
To make a request on this API, make sure you specify the min and max GPS coordinates of the area you want to cover.
This is a world wide database, not only for the US.
aviation.stackexchange.com/users/22341/Anamaria Lupu
This is my first post so bare with me.
I don't know if you are trying to get one region only or a global data set.
The issue is that member states are responsible for their own airspace and thus airport/NAVAID/intersection/waypoint/so-on-and-so-forth location data.
You may want to see about getting a copy of ICAO document
7910 "Manual of ICAO identifiers" This book cost money though.
If you are interested in the North American region (U.S./Mexico/Canada/Caribbean/and-so-on) then you can get for free the FAA Location Identifier book with FAA Order JO 7350.9x.
The lat/long of every waypoint/NAVAID/Airport and the like is in it.
Unlike a previous answer post you don't have to ask for access permission either.
To keep things simple here is a link.
FAA Location Identifiers
That's what I got for you
aviation.stackexchange.com/users/29428/E. Jorgensen
Updating: The link is at https://www.faa.gov/air_traffic/flight_info/aeronav/aero_data/NASR_Subscription/
This provide the text file along with layout data for all the fixes, etc.
The CIFP can be downloaded as well, but the layout is commercialized (~$400).
I have not been able to programmatically download the zip file.
aviation.stackexchange.com/users/42378/Chuck
I wonder if it is possible to download a database with waypoints, navaids, airports and airways between them. I've been working with AIP documents but it's difficult to get raw information from them and they only have information about waypoints.  I happened to find skyvector.com and I thought there would be an easier way to obtain that amount of information.
Where to find a waypoints/fixed points, navaids and airports database?
aviation.stackexchange.com
<icao><website><datasets><navaids><vor>
aviation.stackexchange.com/questions/9681
aviation.stackexchange.com/users/4250/Godraude
OpenFlight, National Flight Data Center, GPX Aviation Waypoint Generator are all waypoints/fixed points, navaids and airports databases Suggested resources include OpenFlights, the National Flight Data Center, opennav.com, the GPX Aviation Waypoint and the FAA Location Identifier book.
Suggested resources include OpenFlights, the National Flight Data Center, opennav.com, the GPX Aviation Waypoint and the FAA Location Identifier book.