I'm looking for some sort of list with most common game resolutions my game should support.
A good place to start is the Steam Hardware Survey which includes a list of the most popular display resolution among Steam users. Wikipedia has a list of common resolutions in computer graphics. You can also look at some commercial games and see what resolutions they allow the user to select from.
If you're going to support any resolution and just want a list to show to the user, you can query the list of supported resolutions on the player's PC. How you do that depends on the API, for example in SDL you'd use SDL_ListModes.
I'm pretty sure on Direct X platforms at least, you're expected to query the platform for a list of available modes (using EnumAdapterModes on the device). That way the platform will already exclude any unavailable resolutions (because the GFX card or OS doesn't support it).
You can further sub-filter those modes to exclude any you don't support (for example if you don't support widescreen resolutions), but you certainly shouldn't be defining your own arbitrary list of resolutions and expecting them to map to the set which is actually available.
Unless you plan to target one machine with one predefined set of resolutions, i'd recommend making your game so that it works on any resolution.
If your game has a high range of resolutions it should support (meaning: from very low to very high) in that case it makes sense to leave out things on lower resolution and also to use different graphics sets (e.g. High def textures make no sense on a small handheldscreen).