What are the endings I can obtain, and how do I obtain them?

Currently (version 1.0.1.4) there are three endings and one post-credits scene that can be unlocked. The endings are in order of obtainability (named after their associated achievements):

• The Hollow Knight - The default ending. To get this ending, kill the Dreamers and enter the Black Egg straight away. Kill the Hollow Knight boss. In this ending you take the place of the Hollow Knight, continuing the cycle. This ending becomes locked after obtaining the Void Heart.
• Dream No More - The golden ending. To get this ending, first obtain a fully awakened Dream Nail by killing the various spirit bosses, the Champion versions of False Knight (Failed Champion), Soul Master (Soul Tyrant) and Broken Vessel (Lost Kin). Additional essence can be gained from the various non hostile spirits and the Dream Trees scattered around the map. You need a total of 1800 essence to fully awaken the Dream Nail (2400 essence is required to hear the Seers last words, but this is optional for this ending). Additionally, go to the Queen's Garden and obtain the White Crest Fragment. After awakening the Dream Nail and obtaining the first half of the Kingsoul, strike the Knight sitting outside the Palace Grounds. This will transport you to the Dream World, where you must complete the difficult White Palace. At the end of the palace, strike the king until his corpse drops from the throne. Optionally, you can go to the right of the king and read his last message or sit on the throne. After striking the King's corpse, you must pick up the other half of the Kingsoul. This will make you leave the Dream World and will kill the Knight. Equip the Kingsoul and enter the Abyss. Go to the bottom most section of the Abyss and enter the newly opened cave area. Descend down the area, killing or dodging the Siblings. At the bottom of the Abyss, strike the mirror with your Dream Nail and ascend from the Abyss in the Dream World. This will change the Kingsoul into the Void Heart. After that go to the Black Egg. Hornet will be waiting outside. Enter the Egg and fight The Hollow Knight. Halfway through the fight, Hornet will interrupt by hitting the Hollow Knight with her nail and tying him down. Hit the Hollow Knight with the Dream Nail. At this point, The Radiance will appear. It is a three stage boss fight. After you complete it, you can watch the ending. In this ending, you kill the Radiance and end the cycle.
• Sealed Siblings - A semi-hidden bad ending. To get this ending, obtain the Void Heart and enter the Black Egg. When Hornet interrupts, don't strike the Hollow Knight with your Dream Nail, but continue your attacks. Hornet will eventually pass out and the fight continues. Beat the Hollow Knight to get this ending. In this ending, you take the Hollow Knights place, but because Hornet is sealed with you, the cycle is ended forever as no new knights can enter the Black Egg and the infection will eventually kill all of bugkind.

Finally, the post-credits scene is obtainable on any ending by talking to Mr. Mushroom seven times in his different locations with the Spore Charm equipped. It shows Mr. Mushroom flying over Dirtmouth while staring at the camera ominously before ending on a "To Be Continued" screen. The associated achievement for this ending is Passing of the age.

The Hollow Knight
Defeat the hollow knight without the void heart.
In this ending you take the place of the hollow knight, and get sealed in the black egg.

Sealed Siblings
Beat the hollow knight with the void heart.
You take place of the hollow knight, and Hornet is on the black egg.

Dream no More
Collect the void heart, and beat the radiance.
Tip: Dream nail the hollow knight while being attacked by Hornet, and defeat the radiance.

Embrace the Void
Unlock embrace the void and defeat radiance.
Tip: Do all the patriots and kill the radiance.

Delicate flower
Beat all pathions have given delicate flower to the Godseeker, and Have defeated Radiance

Mr mushroom takes off
Have found Mr. mushroom in all locations, and defeated any final boss. After the credits you'll see mr. mushroom blast into space getting you an achievement.