Great free programs
IrfanView
The freeware (for non-commercial use) graphics program IrfanView does an excellent job. Among other things it excels at:
- resampling after reducing the size of graphics files.
- Converting files between formats.
- Saving GIF and PNG files with one colour transparent.
- It works with all common formats, including jpg, gif, png, bmp, tif etc.
- It's Vista compatible.
It's a very small program which you can download from here: http://www.irfanview.com/main_download_engl.htm
It's a PC Magazine Editors Choice:
http://www.pcmag.com/article2/0,1759,1589928,00.asp
I use Fireworks, Illustrator, Photoshop and CorelDraw, but I still go back to IrfanView for a lot of resizing and format conversion. It's much faster than the big expensive programs – I keep those for the more advance tasks.
The program:

The above .jpg file has just been resized.
Here are some of the saving options:

If you're saving a .gif or .png file you get an option of choosing the colour to be rendered transparent.
But wait, there's more!
IrfanView also includes a photo slideshow and it displays thumbnail views of a huge array of graphics files including some which many programs don't want to know – like CorelDraw clipart and .wmf files.
If you need more clout...
Check out the gold-plated Photoshop CS3.
For creating graphics from scratch you can't beat the free GIMP for value.