As people who know me will tell you, this is where I mention
GIMP. I find it faster to work with than Photoshop or PSP now that I'm used to the menus. It's very different to typical Windows-y programs, mind, so a lot of people will dismiss it without giving it a chance. I prefer 1.25, but your milage may vary (and 1.25 has a few interesting issues).
Okay, so it's also occasionally spazzy, but so's Photoshop on my computer :p.
I'm not much of a banner/sig maker, though. I prefer my sites near graphic-free and plain, so it's not my thing...I'm sure some people here can take a whack at it for you.