From the rec.puzzles FAQ
Aside from "angry" and "hungry" and words derived therefrom, there is only one word ending with "-gry" in Webster's Third Unabridged: "aggry." However, this word is defective in that it is part of a phrase "aggry beads."
The OED's usage examples all talk about "aggry beads."
Moving to older dictionaries, we find that "gry" itself is a word in Webster's Second Unabridged (and the OED):
gry, n. (L. gry, a trifle; Gr. gry, a grunt)
1. a measure equal to one-tenth of a line. Obs.
2. anything very small. Rare.
(Explanation of references is given at the end of the list.)
aggry (OED:1:182; W2; W3)
Agry Dagh (Mount Agry) (EB11)
ahungry (OED:1:194; FW; W2)
angry (OED; FW; W2; W3)
anhungry (OED:1:332; W2)
Badagry (Johnston; EB11)
Ballingry (Bartholomew:40; CLG:151; RD:164, pl.49)
Croftangry (DFC, as "Chrystal Croftangry")
eard-hungry (CED (see "yird"); CSD)
Echanuggry (Century:103-104, on inset map, Key 104 M 2)
Egry (France; TIG)
gry (from Latin _gry_) (OED:4/2:475; W2)
gry (from Romany _grai_) (W2)
haegry (EDD (see "hagery"))
higry pigry (OED:5/1:285)
hogry (EDD (see "huggerie"); CSD)
hogrymogry (EDD (see "huggerie"); CSD (as "hogry-mogry"))
hongry (OED:5/1:459; EDD:3:282)
huggrymuggry (EDD (see "huggerie"); CSD (as "huggry-muggry"))
hungry (OED; FW; W2; W3)
Hungry Bungry (Daily Illini, in ad for The Giraffe, Spring 1976)
kaingry (EDD (see "caingy"))
land-hungry (OED; W2)
Langry (TIG; Times)
MacLoingry (Phillips (as "Flaithbhertach MacLoingry"))
magry (OED:6/2:36, 6/2:247-48)
Margry (Indians (see "Pierre Margry" in bibliog., v.2, p.1204))
menagry (OED (see "managery"))
overangry (RH1; RH2)
Pelegry (CE (in main index as "Raymond de Pelegry"))
Pingry (Bio-Base; HPS:293-94, 120-21)
podagry (OED; W2 (below the line))
Pongry (Andree (Supplement, p.572))
pottingry (OED:7/2:1195; Jamieson:3:532)
puggry (OED:8/1:1573; FW; W2)
scavengry (OED (in 1715 quote under "scavengery"))
Schtschigry (LG/1:2045; OSN:97)
Seagry (TIG; EB11)
Segry (Johnston; Andree)
Shchigry (CLG:1747; Johnson:594; OSN:97,206; Times:185,pl.45)
Shtchigry (LG/1:2045; LG/2:1701)
skugry (OED:9/2:156, 9/1:297; Jamieson:4:266)
Tchangry (Johnson:594; LG/1:435,1117)
Tingry (France; EB11 (under "Princesse de Tingry"))
toggry (Simmonds (as "Toggry", but all entries are capitalized))
ulgry (Partridge; Smith:24-25)
unangry (OED; W2)
Wirgy (CLG:2090; NAP:xxxix; Times:220, pl.62; WA:948)
yeard-hungry (CED (see "yird"))
yerd-hungry (CED (see "yird"); OED)
yird-hungry (CED (see "yird"))
Ymagry (OED:1:1009 (col. 3, 1st "boss" verb), (variant of "imagery"))
This list was gathered from the following articles:
George H. Scheetz, In Goodly Gree: With Goodwill, Word Ways 22:195 (Nov. 1989)
Murray R. Pearce, Who's Flaithbhertach MacLoingry?, Word Ways 23:6 (Feb. 1990)
Harry B. Partridge, Gypsy Hobby Gry, Word Ways 23:9 (Feb. 1990)
A. Ross Eckler, -Gry Words in the OED, Word Ways 25:4 (Nov. 1992)
(Many references are of the form (Source:volume:page) or (Source:page).)
Andree, Richard. Andrees Handatlas (index volume). 1925.
Bartholomew, John. Gazetteer of the British Isles: Statistical and Topographical. 1887.
BBC = BBC Pronouncing Dictionary of English Names.
Bio-Base. (Microfiche) Detroit: Gale Research Company. 1980.
CE = Catholic Encyclopedia. 1907.
CED = Chambers English Dictionary. 1988.
Century = "India, Northern Part." The Century Atlas of the World. 1897, 1898.
CLG = The Colombia Lippincott Gazetteer of the World. L.E.Seltzer, ed. 1952.
CSD = Chambers Scots Dictionary. 1971 reprint of 1911 edition.
Daily Illini (University of Illinois at Urbana-Champaign).
DFC = Dictionary of Fictional Characters. 1963.
EB11 = Encyclopedia Britannica, 11th ed.
EDD = The English Dialect Dictionary. Joseph Wright, ed. 1898.
France = Map Index of France. G.H.Q. American Expeditionary Forces. 1918.
FW = Funk & Wagnalls New Standard Dictionary of the English Language. 1943.
HPS = The Handbook of Private Schools: An Annual Descriptive Survey of
Independent Education, 66th ed. 1985.
Indians = Handbook of American Indians North of Mexico. F. W. Hodge. 1912.
Jamieson, John. An Etymological Dictionary of the Scottish Language. 1879-87.
Johnston, Keith. Index Geographicus... 1864.
LG/1 = Lippincott's Gazetteer of the World: A Complete Pronouncing Gazetteer
or Geographical Dictionary of the World. 1888.
LG/2 = Lippincott's New Gazetteer: ... 1906.
Lipp = Lippincott's Pronouncing Gazetteer of the World. 1861, undated
edition from late 1800's; 1902.
NAP = Narodowy Atlas Polski. 1973-1978 (Polish language)
OED = The Oxford English Dictionary. 1933. (Form: OED:volume/part number if
OSN: U.S.S.R. Volume 6, S-T. Official Standard Names Approved by the United
States Board on Geographic Names. Gazetteer #42, 2nd ed. June 1970.
Partridge, Harry B. "Ad Memoriam Demetrii." Word Ways, 19 (Aug. 1986): 131.
Phillips, Lawrence. Dictionary of Biographical Reference. 1889.
RD = The Reader's Digest Complete Atlas of the British Isles, 1st ed. 1965.
RH1 = Random House Dictionary of the English Language, Unabridged. 1966.
RH2 = Random House Dictionary of the English Language, Second Edition
Simmonds, P.L. Commercial Dictionary of Trade Products. 1883.
Smith, John. The True Travels, Adventvres and Observations: London 1630.
Stieler, Adolph. Stieler's Handatlas (index volume). 1925.
TIG = The Times Index-Gazetteer of the World. 1965.
Times = The Times Atlas of the World, 7th ed. 1985.
W2 = Webster's New International Dictionary of the English Language,
Second Edition, Unabridged. 1934.
W3 = Webster's Third New International Dictionary of the English Language,
WA = The World Atlas: Index-Gazetteer. Council of Ministires of the USSR, 1968.
Worcester, J.E. Universal Gazetteer, Second Edition. 1823.
However, the riddle you hear may be wrong
Jerry Taylor writes:
Here is the riddle in its original form:
"Think of words ending in -GRY. Angry and hungry are two of them. There are only three words in the English language. What is the third word? The word is something that everyone uses every day. If you have listened carefully, I have already told you what it is."
In its proper, original form, the first two sentences have absolutely nothing to do with the question: "Think of words ending in -GRY. Angry and hungry are two of them." Ignore those two sentences. They are there only to throw you off course. (And it worked, didn't it?) What's left
is the actual riddle itself: "There are only three words in the English language. What is the third word? The word is something that everyone uses every day. If you have listened carefully, I have already told you what
it is." The key is the phrase "the English language." In this three-word phrase, the third word is simply the word "language." Get it? "Language" is definitely something that "everyone uses every day"! Without that
quirky little twist, the puzzle would be just another trivia question, not a riddle.