It is important to not just give up when the adaptor/converter doesn't seem to work out of the box. Most probably there will be converters which won't work and VGA displays which won't be supported, but my feeling is most of them work just fine - with some extra steps.
If you want to check whether yours has chances, use an empty
/boot/config.txt file and add
hdmi_safe=1 to it.
While this won't give you the best resolution, it probably will get you to the login prompt.
After that you can start with tweaking it further until you get the most out of your monitor capabilities.
You can get some useful information about your monitor by entering these 3 commands:
/opt/vc/bin/tvservice -m CEA
/opt/vc/bin/tvservice -m DMT
Use the Raspberry Pi Video Modes reference link to yield the above results and finetune.
After rebooting the Pi, your monitor firmware might show errors like 'out of sync' or 'resolution not supported'. Lower the resolution and/or refresh rate and try again.
After testing I got good results even with small Chinese $3 adaptors connected to the cheapest monitors available in the shop. Out of the box the converter gave a blank screen with the monitor going into powersave mode seconds after. After following the above steps my
/boot/config.txt now shows: