The Opera Omnia 
Euler's books and publications 
Euler's correspondence 
Euler's life 
Euler's work 
Background on 18th century science 
Published by Birkhäuser and the Euler Commission of Switzerland, the Opera Omnia is the definitive printed source for Euler's works. Publication began in 1911, growing to scores of volumes comprising nearly all of Euler's works.
Put simply, the Opera Omnia is the authoritative source of Euler's works. Not only do his writings appear in neatly typeset, edited form, but each volume also includes commentariessome of them very lengthy and very scholarlyon those works. The Opera Omnia can be found in many large research libraries, and is well worth the time spent with it. Most recently, Springer has been publishing volumes of Euler's correspondence, and has several more volumes in preparation. 
John Blanton's impressive translation of Euler's Introductio in analysin infinitorum (E101). 
John Blanton's translation of the first nine (of 27) chapters of Euler's Institutiones calculi differentialis (E212). 
Also known as "Letters to a German Princess," several volumes of this work have been published over the last half century. The most recent edition is a 1997 reprint by Thoemmes Continuum, featuring an English translation by Henry Hunter, and a new introduction by Andrew Pyle. This edition can be puchased at the Thoemmes Website. 
Once again, the Euler scholar should turn first to the Opera Omnia. Series IV A is a comprehensive
list of Euler's letters, describing every letter known and kept at the University of Basel. Volumes in this series are organized as follows:

This is a threevolume collection of Euler's correspondence sent between the Berlin and St. Petersburg
Academies. AkademieVerlag in Berlin, 1959, 1961, and 1976.

This work by Fuss contains extensive correspondence between Euler, Goldbach, and Bernoulli, among others. 
Published for the 250th anniversary of Euler's birth (two years early), this work contains the complete correspondence between Euler and Goldbach. 
In this book, Eric Forbes presents the 31 known letters in the correspondence between Euler and Tobias Mayer, all translated into English, with commentary and notes. 
Some of Euler's correspondence with Stirling is published, in English translation, in this book on Stirling. 
Engelsman's book contains a manuscript of Euler's published in English and Latin. 
This is the first biography of Euler available in the English language. Calinger's work is very comprehensive, providing a full narrative of Euler's life and career, with ample citation and a generous bibliography. 
A chronological recounting of Euler's life, Fellmann's work is a very accessible biography of Euler, and avoids technical details by being "entirely formula free". This book contains much interesting information, though it is rather short (156 pages). This biography was originally written in German, but an English translation by Erika and Walter Gautschi was published by Birkhäuser in 2007. 
The first modern biography of Euler. Thiele's work is a concise (110 pages) but interesting read. Thiele's work is a much more balanced biography than those from the early 20th century (cf. du Pasquier, below). This biography is written in German, and has not been translated into English. 
This is a very short (24 pages) and little known (we've never seen it referenced) biography of Euler, written as part of BirkhäuserVerlag's Kurze MathematikerBiographien series. 
A complete, but slightly eulogistic, biography of Euler published in French, this book also contains some good information about Euler's contemporaries. This book has long been out of print, but it is being reprinted, along with a translation (Euler and his Friends) by John Glaus of The Euler Society in 2008. 
Paperback, bound with staples, approximately 6" x 9". A short 15page biography of Euler in German. This booklet is a reprint of the text of an address that Rudio gave in 1883 at a celebration of the 100th anniversary of Euler's death. Rudio was a founding member of the editorial committee of the Opera Omnia and edited several of the early volumes, including some on number theory. 
Description from Amazon.com:
The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment's most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world's best Eulerian scholars from seven different countries about Euler, his life and his work.

Description from MAA Online:
The Early Mathematics of Leonhard Euler describes Euler's early mathematical works: the 50 mathematical articles he wrote before he left St. Petersburg in 1741 to join the Academy of Frederick the Great in Berlin. These works contain some of Euler's greatest mathematics: the Konigsburg bridge problem, his solution to the Basel problem, his first proof of the EulerFermat theorem. It also presents important results that we seldom realize are due to Euler: that mixed partial derivatives are equal, our f(x) notation, and the integrating factor in differential equations. The book provides some of the way mathematics is actually done. For example, Euler found partial results towards the EulerFermat theorem well before he discovered a proof of the Fermat theorem itself, and the EulerFermat version came 30 years later, beyond the scope of this book. 
Description from MAA Online:
This book celebrates the 300th birthday of Leonhard Euler (1707  1783), one of the brightest stars in the mathematical firmament. The book stands as a testimonial to a mathematician of unsurpassed insight, industry, and ingenuity  one who has been rightly called "the master of us all." The collected articles, aimed at a mathematically literate audience, address aspects of Euler's life and work, from the biographical to the historical to the mathematical. The oldest of these was written in 1872, and the most recent dates to 2006. 
Reknowned mathematics author William Dunham's book is the most complete examination in English of Euler's mathematical work. Written for the mathematically literate (The reader should be familiar with calculus), Dunham examines selected mathematics of Euler, and places his work in a historical context. Over eight chapters, Dunham looks separately at some of Euler's contributions to Number Theory, Logarithms, Infinite Series, Analytic Number Theory, Complex Variables, Algebra, Geometry, and Combinatorics. Dunham's book also contains a brief biography of Euler. 
Perhaps the longest full discussion in English of Euler's science and mathematics, the Euler entry in The Dictionary of Scientific Biography runs 17 pages, and is an excellent resource. 
Description from a review by Ed Sandifer:
In an era when most Euler scholarship was done in the Soviet Union and in the DDR, Truesdell kept the candle lit in the West, though his work and his personality were both controversial... This volume contains 42 "Fugitive essays", about a third of which directly concern Euler, and more than half of the rest involving Euler indirectly.... the Fugitive Essays ought to be required reading for anyone trying to understand Euler. They are entertaining, opinionated, well informed and at times controversial. 
While not explicitly about Euler's mathematics, his work does come up often in this interesting, though technical, book on the constant gamma (γ). 
An English translation of Optica in de eeuw can Euler (published in Dutch, 1986), Hakfoort's book is a careful look at the role played by Euler's Nova theoria lucis et colorum (see E88) in the development of 18th Century Optics. Those interested in closely examining Euler's impact on 18th Century Science should consider this required reading. 
Published for the 200th anniversary of Euler's death, this multilingual volume (English, French, and German) contains thirty essays on Euler's life and work. 
Proceedings of a conference on the 200th anniversary of Euler's death, this festakt contains 16 essays on Euler's life and work. One of these is written in English; the rest are in German. 
Another collection of essays (in German), this one published for the 250th anniversary of Euler's birth. 
A fantastic resource! Includes a detailed accounting of the development of Academybased science in the 18th century, as well as a list of all major private, public, and semipublic academic institutions in Europe for the same time period. 
A readable biography of PierreLouis Moreau de Maupertuis; also includes a good deal of information regarding the development of the Berlin Academy, and some information on Euler's experiences in Berlin. 
A comprehensive resource on the history of the St. Petersburg Academy as well as on general cultural, social and political developments in the Russian Empire, up to 1917. 