Different tools are appropriate for different tasks:
Some choices for image touch-up (and sometimes raster painting) are:
http://www.adobe.com/products/photoshop/main.html (best known, most expensive, windows or mac, about $600, though PhotoShop Elements is much cheaper at around $50)
Macromedia Fireworks (windows and mac)
ImageJ http://rsb.info.nih.gov/ij/ (java, all platforms, free public domain
http://www.iview-multimedia.com/ (Mac only, $160. sort of a better iPhoto.)
http://www.lightboxsoftware.com/ (Mac only. shareware/$25. photo management only.)
http://www.jasc.com/products/paintshoppro/ (30-day free eval, windows only, about $100)
http://rsb.info.nih.gov/nih-image/about.html (Mac Class, public domain, in pascal, inspiration for ImageJ)
http://www.jphotobrushpro.com/ (java, all platforms, $25)
http://www.gimp.org (free open source; available for windows and unix)
http://www.cinepaint.org (free open source; available for windows and unix; oriented around film (motion or still) work. based on an old GIMP version, so unless need huge ranges, go with gimp first. does four 32-bit channels (128-bit color), and uses CMYK not RGB.)
http://www.trilon.com/xv/ (shareware free/$25; unix. no painting, just image editing.)
http://www.apple.com/iphoto (free with mac)
PhotoLine http://www.pl32.com/endocs/starten.htm (windows and mac, about $60)
Color It! (mac OS 9 only, about $50)
www.caffeinesoft.com (mac only; free downloads after they went out of business)
Corel Painter (mac and windows $299)
Corel Photo-Paint ftp://ftp2.corel.com/pub/linux/PhotoPaint9/ ftp://ftp.zdf.de/pub/3satdownload/CorelPHOTOPAINT9Lnx.tar.gz (linux, free download, has ICC support and CMYK color)
SCO Caldera Camelero Light (linux, ICC support and CMYK color)
Hancom Painter http://en.hancom.com/products/hancompainter.html (linux, $60 for whole office package)
I personally find both PhotoShop and GIMP to be impenetrable, but again, I don't use them much.
Some vector-oriented drawing tools include:
Adobe Illustrator
Macromedia Freehand
CorelDRAW
Visio
Sodipodi http://www.sodipodi.com/ (GPL free, unix and windows, SVG is native. has integration with autotrace)
Inkscape http://www.inkscape.org/ (GPL free, unix gtk; fork from Sodipodi http://article.gmane.org/gmane.comp.graphics.sodipodi/1055)
Sketch http://sketch.sourceforge.net/ (free, unix, in python)
Mayura Draw http://www.mayura.com/ (shareware $39 windows)
Karbon14 http://www.koffice.org/karbon/ (GPL free, unix, to be part of KOffice, replacing KIllustrator/Kontour)
Dia http://www.lysator.liu.se/~alla/dia/ (GPL free, unix, like visio)
ImPress http://www.ntlug.org/~ccox/impress/ (linux, open source, tcl/tk)
Ipe http://ipe.compgeom.org/ (GPL, unix, QT; oriented around Latex)
Bitflash Brilliance http://www.bitflash.com/products/brilliance.asp (SVG editor, pricing and platform?)
EazyDraw (mac only, $95)
A list of vector and raster drawing tools for unix may be found at:
http://www.linuxartist.org/2d.php
A long list of (commercial) graphics tools for OS X can be found at:
http://www.apple.com/downloads/macosx/imaging_3d/
For image conversion and optimization, any of the above image touch-up products above will do it.
There are also specialized programs which are typically easier and more capable for that use:
http://www.imagemagick.org/ (free open source, all operating systems)
DeBabelizer (windows and mac, about $450)
http://www.lemkesoft.com/en/graphcon.htm (mac, free with OS and $30 upgrade)
There are some free online web-based image tools:
http://www.imagemagick.net/MagickStudio/scripts/MagickStudio.cgi
http://www.gifworks.com/
Some lower-level unixy free image related products are:
GD (http://www.boutell.com/gd/). more of a library for use from languages
like Perl, though PerlMagick does this too. See http://www.stonehenge.com/merlyn/WebTechniques/col47.html using it to generate rounded corners.
NetPBM (http://netpbm.sourceforge.net/). like ImageMagick but based on many small programs, which mostly only work in PBM.
gFONT http://www.engelschall.com/sw/gfont/ . Makes GIF images of texts in any font supported by TeX.
pstoedit http://www.pstoedit.net/pstoedit . GPL free. converts PS and PDF to other vector formats. GsView can be used as gui
autotrace http://autotrace.sourceforge.net/ . GPL free. will trace bitmaps to form vector graphics. works well with pstoedit
On the Mac, the supplied Preview will read pdf, ps, and eps and will export several image formats including png and jpeg. (Note that the EPS standard says that it can contain a fixed size binary header prior to the "%!PS-Adobe-3.0 EPSF-3.0", which is used to hold an offset to an image preview, but some tools such as peps and eps2png don't handle that. ImageMagick convert does.)
For information about image compression for the web, see: http://www.brycetech.com/tutor/windows/jpeg_compression.html