There are actually more than three words which end in -gry, but almost all of them have fallen out of common usage. The two words ending in -gry which have survived and are still commonly used are both adjectives: hungry and angry. When this particular brain teaser was first created, at least two other words ending in -gry were still in somewhat common use: meagry and aggry. Meagry referred to being meager, while aggry were polished stones used in some African jewelry.
The problem with the -gry riddle today is that even those two words have fallen out of popular usage, leaving only angry and hungry. There is no readily available answer for the third common word ending in -gry. The original -gry brain teaser is now often presented as more of a trick question than an actual riddle.
One popular variation on the original -gry riddle depends on the listener's powers of observation. The storyteller begins by telling the listener about two common words ending in -gry, which the listener may readily identify as "hungry" and "angry". In this form of the -gry riddle, the storyteller goes on to say there are only three words in "the English language". The storyteller asks the listener to name the third word, assuring him or her that the answer has already been provided. The correct answer is "language", since it is the third word in the phrase "the English language".
Other variants on the original -gry riddle also hinge on this deceptive language. The storyteller may ask the listener to name three words which end in "gree". The listener may come up with both hungry and angry, but draw a blank on the third -gry word. The correct answer in this case is agree, since the storyteller usually finishes the riddle by saying 'you will agree I've provided the answer already.' The listener may only be thinking of the literal -gry ending, while the storyteller was implying the phonetic sound of 'gree'.
There are other variations of the -gry riddle available on the Internet and in puzzle book collections. While a few may require researching archaic dictionaries for examples of actual words ending in -gry, most of these riddles only use the original -gry question as a distraction from the real word puzzle.