Here are some articles related to Fermat's Last Theorem. Be aware that there
is some of overlap between categories.
THE BIG THREE
"On modular representations of Gal(Q-bar/Q) arising from modular forms",
by Kenneth Ribet; Inventiones Mathematicae 100 (1990), pages 431-476.
This article contained the first complete substantiation
of Gerhard Frey's guess; it shows that Fermat's Last
Theorem is implied by the Taniyama-Shimura-Weil Conjecture.
"Modular elliptic curves and Fermat's Last Theorem," by Andrew Wiles;
Annals of Mathematics, Volume 141 (1995), pages 443-551.
This article contains most of the ideas developed by Wiles
to prove the semi-stable case of the TSW conjecture (and
with it Fermat's Last Theorem).
"Ring-theoretic properties of certain Hecke algebras", by Richard Taylor
and Andrew Wiles; Annals of Mathematics, Volume 142 (1995), pages 553-572.
This companion article proves the extra results that were needed
in order to repair Wiles' flawed proof of 1993.
BIOGRAPHICAL-HISTORICAL
"Wiles Receives NAS Award in Mathematics"; Notices of the American Mathematical
Society, Volume 43 (July 1996), pages 760-763.
Information on Wiles' early career.
"Yutaka Taniyama and his time: very personal recollections", by Goro Shimura;
Bulletin of the London Mathematical Society, Volume 21 (1989), pages 186-196.
Taniyama's life and work, as described by the colleague
who knew him best.
"Steele Prize for Lifetime Achievement: Goro Shimura"; Notices of the
American Mathematical Society, Volume 43 (November 1996), pages 1343-1347.
1301-1307.
Shimura's life and work.
"Working with Numbers in the Seventeenth and Nineteenth Centuries", by
Catherine Goldstein; pages 344-371 in "A History of Scientific Thought",
edited by Michel Serres, Blackwell (1995).
Goldstein does great job comparing the different milieus in
which Fermat and Kummer worked.
"How Math Can Save Your Life", by Simon Singh; Math Horizons, February
1998, pages 5-7.
Singh retells the famous story about Paul Wolfskehl. Too bad
it's (probably) not true! See:
"Paul Wolfskehl and the Wolfskehl Prize", by Klaus Barner; Notices of the
American Mathematical Society, Volume 44 (November 1997), pages 1294-1303.
A different view of Paul Wolfskehl (from someone who ought to know).
"Some history of the Shimura-Taniyama Conjecture", by Serge Lang; Notices
of the American Mathematical Society, Volume 42 (November 1995), pages
1301-1307.
Lang doesn't think that Weil deserves to have his name
attached to the conjecture; here he says why.
NEWS STORIES
"Fermat's Theorem", by James Gleick; The New York Times Magazine, October 3,
1993, pages 52-53.
How Gleick can convey so much of the true nature of
mathematics in less than a page and a half beats me!
"The World's Most Famous Math Problem Has Finally Been Solved ... Or Has It?",
by Marilyn vos Savant; Parade Magaine, November 21, 1993, page 10.
For those who don't want to take the time to read her book,
you can see here some of vos Savant's confusions, written
in her usual breezy and engaging style.
"Fame by Numbers", by Ian Katz, The Guardian Weekend, April 8, 1995,
pages 34-42.
This is one of the best popular-press accounts of the problem
that I've seen. Katz is a lively writer who captures the
personalities of the people in his story and gets the important
mathematical and historical facts straight.
"Andrew Wiles: A Math Whiz Battles 350-Year-Old Puzze", by Gina Kolata;
Math Horizons, Winter 1993, pages 8-11.
"Fermat's Last Stand", by Simon Singh and Kenneth A. Ribet; Scientific
American, November 1997, pages 68-73.
TECHNICAL-EXPOSITORY
"Fermat's Last Theorem", by Harold M. Edwards; Scientific American, some
year or other, pages 104-122.
"Fermat's Last Theorem and Modern Arithmetic", by Kenneth A. Ribet and
Brian Hayes; The American Scientist, Volume 82 (March-April 1994),
pages 144-156.
"Introduction to Fermat's Last Theorem", by David A. Cox; The American
Mathematical Monthly, January 1994, pages 3-14.
"A Marvelous Proof", by Fernando Q. Gouv\^ea; The American Mathematical
Monthly, March 1994, pages 203-222.
All three articles are worth reading.
"Number Theory as Gadfly", by Barry Mazur, The American Mathematical Monthly,
Volume 98 (1991), pages 593-610.
A great article for the general mathematician, explaining the
attraction of number theory.
"Polynomial Pursuits: Questioning Answers", by Barry Mazur; Quantum, volume 7,
no. 3 (January 1997), pages 4-9,27.
A great article for undergraduates or advanced high school
students, introducing them to the joys of elliptic curves.
TECHNICAL
"From the Taniyama-Shimura conjecture to Fermat's last theorem", by
Kenneath A. Ribet; Annales de la Facult\'e des Sciences de Toulouse
Math. (5) 11 (1990), pages 116-139.
This is heavy going, but it's the best available introduction
to the part of the proof of Fermat's Last Theorem that is
all too often neglected.
"A report on Wiles' Cambridge lectures", by K. Rubin and A. Silverberg;
Bulletin of the American Mathematical Society, Volume 31 (1994), pages 15-38.
"Fermat's Last Theorem", by Henri Darmon, Fred Diamond, and Richard Tayor;
in Current Developments in Mathematics, 1995, International Press,
pages 1-107.
This article comes to me highly recommended.
"The Shimura-Taniyama Conjecture (d'apre\`es Wiles)", by Henri Darmon;
Mongraphies CICMA Lecture Notes 1994-02.
"Galois representations and modular forms", by Kenneth Ribet;
Bulletin of the American Mathematical Society, Volume 32 (1995), pages 375-402.
"An elementary introduction to the Langlands programme", by Stephen Gelbart;
Bulletin of the American Mathematical Society, Volume 10 (1984), pages 177-219.
"Old and new conjectured Diophantine inequalities", by Serge Lang; Bulletin
of the American Mathematical Society, Volume 23 (1990), pages 37-75.
I remember the lecture that Lang gave on this topic in the late
1980's; I came out with the wondering realization that I'd
probably live to see FLT proved. See page 39 for a nice proof
of "Fermat's Last Theorem for polynomials". Also see page 47
for one of Lang's famous diagrams, showing FLT "menaced" on all
sides by arrows connecting it to mainstream conjectures.
"Generalized non-abelian reciprocity laws: putting Wiles's achievement into
context," by Avner Ash and Robert Gross; the amstex-source is available at
http://fmwww.bc.edu/MT/gross/avner.tex.txt .
OTHER
"A generalization of Fermat's Last Theorem: The Beal Conjecture and
prize problem", by R. Daniel Mauldin; Notices of the American Mathematical
Society, Volume 44 (December 1997), pages 1436-1437.
The problem is not entirely new, but no one has ever
offered money for it before.
Review of "The mathematical career of Pierre de Fermat, by M. S. Mahoney",
by Andr\'e Weil; Bulletin of the American Mathematical Society, Volume 79
(1973), pages 1138-1149.
Weil's attack on Mahoney's book is a bit one-sided (in
my opinion), but nearly all of his points are valid.
Weil is not only one of the greatest living mathematicians
but he is also a formidable historian.
"Conjecture", by Barry Mazur; Synthese 111, pages 197-210 (1997).
A marvelous explanation of the role of conjecture in
modern number theory.