A font provides a number of glyphs. In order that the glyphs may be printed, they are _encoded_, and the encoding is used as an index into tables within the font. For various reasons, Knuth chose deeply eccentric encodings for his Computer Modern family of fonts; in particular, he chose different encodings for different fonts, so that the application using the fonts has to remember which font of the family it's using before selecting a particular glyph.
When TeX version 3 arrived, most of the drivers for the eccentricity of Knuth's encodings went away, and at TUG's Cork meeting, an encoding for a set of 256 glyphs, for use in TeX text, was defined. The intention was that these glyphs should cover “most” European languages that use Latin alphabets, in the sense of including all accented letters needed. (Knuth's CMR fonts missed things necessary for Icelandic and Polish, for example, which the Cork fonts do have, though even Cork encoding's coverage isn't complete.) LaTeX refers to the Cork encoding as T1, and provides the means to use fonts thus encoded to avoid problems with the interaction of accents and hyphenation (see hyphenation of accented words).
The first MetaFont-fonts to conform to the Cork encoding were the EC fonts. They look CM-like, though their metrics differ from CM-font metrics in several areas. They have long been regarded as “stable” (in the same sense that the CM fonts are stable: their metrics are unlikely ever to change). Each EC font is, of course, roughly twice the size of the corresponding CM font, and there are far more of them than there are CM fonts. The simple number of fonts proved problematic in the production of Type 1 versions of the fonts, but EC or EC-equivalent fonts in Type 1 or TrueType form (the latter only from commercial suppliers). Free auto-traced versions - the CM-super and the LGC fonts, and the Latin Modern series (rather directly generated from Metafont sources), are available.
Note that the Cork encoding doesn't cover mathematics (so that no “T1-encoded” font families can not support it). If you're using Computer-Modern-alike fonts, this doesn't actually matter: your system will have the original Computer Modern mathematical fonts (or the those distributed with the Latin Modern set), which cover “basic” TeX mathematics; more advanced mathematics are likely to need separate fonts anyway. Suitable mathematics fonts for use with other font families are discussed in “choice of scalable fonts”.
The EC fonts are distributed with a set of “Text Companion” (TC) fonts that provide glyphs for symbols commonly used in text. The TC fonts are encoded according to the LaTeX TS1 encoding, and are not necessarily as “stable” are the EC fonts are. Note that modern distributions tend not to distribute the EC fonts in outline format, but rather to provide Latin Modern for T1-encoded Computer Modern-style fonts. This can sometimes cause confusion when users are recompiling old documents.
The Cork encoding is also implemented by virtual fonts provided in the PSNFSS system, for Adobe Type 1 fonts, and also by most other such fonts that have been developed (or otherwise made available) for use with (La)TeX.
Note that T1 (and other eight-bit font encodings) are superseded in
the developing TeX-family members XeTeX and
LuaTeX, which use Unicode as their base encoding,
and use Unicode-encoded fonts (typically in
otf formats). The cm-unicode fonts carry the
flag in this arena, along with the Latin Modern set.