Software for manipulating scales and tunings

Scala - the de facto standard software for creating, manipulating and analyzing tunings
- Wikipedia article on Scala
- instructions for Creating Scala scl files for rank two temperaments

alt-tuner - a tuning plug-in that does adaptive tunings, on-the-fly retuning, and scale analysis by Kite Giedraitis
Fractal Tune Smithy & Bounce Metronome - by Robert Walker
Scala to TUN and MTS online converter - by MicrotonalSoftware.com
scalemap - drop-in microtonal note-to-frequency mapping functionality for C, C++, and Javascript
Temperament finder - site by Graham Breed
Tonescape - Music composition, analysis and educational tool by Joe Monzo

Browser-based tuning tools (JavaScript etc.).

Animated MOS ring demo
Diatonic Scale Explorer - Visualize the diatonic scale with different sizes of fifths
edjiruler v0.0.1 - Visualize JI intervals close to equal divisions of whole numbers
Frequency Explorer - a browser-based synthesizer + sequencer with precisely-configurable musical scale and harmonic spectrum
Harmonic Entropy Calculator - Interactive Harmonic Entropy curves.
Hexagonal Keyboard Demo^{[dead link]} - by Sjoerd Visscher
Interval calculator - a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too
JI Scale Interval Calculator - Shows a list of all JI intervals in your JI scale
Just Intonation -> EDO calculator
Microtonal Software Scale Tree - ET Scale Tree Playground
Microtonal-tuner - Wilckerson Ganda's tuner for all EDOs and EDONOIs (be sure to use https: not http:)
Microtone^{[dead link]} - A HTML5 uniform keyboard demo with any equal temperament
The Monochord^{[dead link]} - Try out just intervals from a base frequency.
MOSedo - Moments of Symmetry in equal divisions of the octave calculator
Music Calculators | Jeremiah Goyette (mostly set calculators)
Offtonic Microtonal Synth
Online 19-edo keyboard
Online H-System Calculators - Hunt Intonation Quality Grade Point Average (IQGPA) Calculator
Online Terpstra keyboard (isomorphic hexagonal keyboard)
Rank 2 Regular Temperament Generator - generate rank2 regular temperaments
Rational Keyboard - JI keyboard with keys that grow in size
Scale Workshop - Generate tuning files in your browser
Selected just intervals by error
Selected just intervals by error (MediaWiki output)
Table of edo intervals
Tempered out comma finder
Tempering out edo finder
Tonespiral - Listen to harmonics visualized as a spiral
Wickisynth - tuning demo synthesizer with Wicki-Hayden key layout
Wolfram Alpha Regular Temperament Widgets
Xen-calc An interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.
Xenpaper.com - A text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around

Useful tools for math in general

Cents to Ratio Calculator - and much more! Also, another one with extensive instructions.
Continued Fraction Calculator
Fast Decimal to Fraction Approximations
Fraction Calculator — An Android app that User:PiotrGrochowski recommends to install. Allows to do arithmetic on fractions, while not outputting a mixed fraction.
Fraction Expression Calculator - easily do ratio arithmetic
Least Common Denominator of Fractions (LCD) Calculator - put your JI ratios in here!
Number To Fractions — Finds fractions to a number that improve over the previous. Allows restricting to 3–limit, 5–limit, 7–limit, 11–limit or 13–limit. Type a number to be approximated by JI ratios, or the binary logarithm of a ratio to be approximated by edo intervals.
Octave - a free, open source equivalent to MATLAB; useful for working with matrices and much more
Online LaTeX Equation Editor - create mathematical expressions in LaTeX format for wiki pages etc.
Wolfram Alpha - perform a variety of intensive mathematical calculations in your browser