A selection of sources for interesting reading in mathematics (in no particular order and by no means exhaustive!)

BOOKS

Theoni Pappus, The Joy of Mathematics, More Joy of Mathematics, Mathematical Scandals
William Dunham, Journey Through Genius, Euler The Master of Us All
Eli Maor, e: The story of a number, To Infinity and Beyond, Trigonometric Delights
David Berlinski, A Tour of the Calculus
GH Hardy, A Mathematician’s Apology
Paul Hoffman, Archimedes’ Revenge, The Man Who Loved Only Numbers
Ian Stewart, The Mathematical Tourist, Islands of Truth, etc.
Raymond Smullyan, What is the Name of This Book, This Book Has No Name, Alice in Puzzleland, The Lady or The Tiger, To Mock A Mockingbird, etc.
Martin Gardner, Diversions from Scientific American, Mathematical Circus, Mathematical Carnival, Mathematical Magic Show, aha! Insight, ah! Gotcha, etc.
Hans Rademacher and Otto Toeplitz, The Enjoyment of Mathematics
James Glueck, Genius
Richard Friedberg An Adventurer’s Guide to Number Theory
Solomon Golomb, Polyominoes
Edwin Abbott, Flatland
Richard Rusczyk and Sandor Rehovsky, The Art of Problem Solving
John D. Barrow, Pi in the Sky
Underwood Dudley, The Trisectors, Mathematical Cranks
Wayne Wickelgren, How to Solve Problems
Loren Larson, Problem Solving Through Problems
George Gamov, One, Two Three, Infinity, Mr Tompkins…
Robert Kanigel, The Man Who Knew Infinity
Douglas Hoffstadter, Goedel, Escher, and Bach, Metamagical Themas
Ross Honsberger, Ingenuity in Mathematics, etc.
George Polya, How to Solve It
Eugene Krause, Taxicab Geometry
Fascinating Fibonaccis (author unknown)
Martha Sved, Journey into Geometries
The Trachtenberg System of Speed Mathematics
Courant and Robbins, What is Mathematics
David Wells, You are a Mathematician
Mayme Logsdon, A Mathematician Explains
Paul Nahim, : An Imaginary Tale
John Allen Paulos Innumeracy, Beyond Numeracy, A Mathematician Reads the Newspaper, Once Upon a Number, etc.
Donald Knuth Surreal Numbers
Conway and Guy The Book of Numbers
Bruce Schechter My Brain is Open
Peter Hilton, Derek Holton, Jean Pederson, Mathematical Reflections
Edward B. Burger Exploring the Number Jungle
Morris Kline any of his books which seem to talk about mathematics in their historical context.
Paul Hoffman, The Man Who Loved Only Numbers

JOURNALS and magazines as sources for reading

Discover
Crux Mathematicorum
Quantum
Math Horizons
Mathematics Magazine
College Mathematics Journal
The Mathematics Teacher
The Arithmetic Teacher
Mathematics & Informatics Quarterly
Science
Scientific American
American Mathematics Monthly
Notices of the American Mathematical Society