Better script fonts for maths

The font selected by \mathcal is the only script font ‘built in’. However, there are other useful calligraphic fonts included with modern TeX distributions.

Euler
The eucal package (part of most sensible TeX distributions; the fonts are part of the AMS font set) gives a slightly curlier font than the default. The package changes the font that is selected by \mathcal.

Type 1 versions of the fonts are available in the AMS fonts distribution.

RSFS
The mathrsfs package uses a really fancy script font (the name stands for “Ralph Smith’s Formal Script”) which is already part of most modern TeX distributions (Type 1 versions of the font are also provided, courtesy of Taco Hoekwater). The package creates a new command \mathscr.
Zapf Chancery
is the standard PostScript calligraphic font. There is no package but you can easily make it available by means of the command
\DeclareMathAlphabet{\mathscr}{OT1}{pzc}%
                                 {m}{it}
in your preamble. You may find the font rather too big; if so, you can use a scaled version of it like this:
\DeclareFontFamily{OT1}{pzc}{}
\DeclareFontShape{OT1}{pzc}{m}{it}%
             {<-> s * [0.900] pzcmi7t}{}
\DeclareMathAlphabet{\mathscr}{OT1}{pzc}%
                                 {m}{it}

Adobe Zapf Chancery (which the above examples use) is distributed in any but the most basic PostScript printers. A substantially identical font (to the extent that the same metrics may be used) is available from URW, called URW Chancery L: it is distributed with Ghostscript, and as part of the “URW base35” bundle, which is available in most distributions.

Examples of the available styles are available on CTAN.
eucal.sty
fonts/amsfonts/latex/eucal.sty
euler fonts
fonts/amsfonts/sources/euler (or browse the directory)
euler fonts, in Type 1 format
fonts/amsfonts/ps-type1/
ghostscript
Browse support/ghostscript/
mathrsfs.sty
Distributed as part of macros/latex/contrib/jknappen (or browse the directory)
rsfs fonts
fonts/rsfs (or browse the directory)
Script font examples
info/symbols/math/scriptfonts.pdf
URW Chancery L
Distributed as part of fonts/urw/base35 (or browse the directory)

This question on the Web: http://www.tex.ac.uk/cgi-bin/texfaq2html?label=scriptfonts