To me, the best software for designing exists between your ears, and the capabilities of CSS; anything else is a bunch of grade A farm fresh manure.
Drawing goofy pictures before you have semantic markup and a working CSS layout is -- to me -- putting the cart before the horse and results in buggy, slow loading, inaccessible sites that really have no business being deployed on the web. To be brutally frank the vast majority of people who start out their "design" process in Photoshop, Gimp, Illustrator, Fireworks, etc generally don't know enough about HTML, CSS, emissive colourspace, accessibility, or the limitations of the medium to be designing but two things...
The design process I advocate is called "Content FIRST" -- which is why the first and foremost tool in my box is a flat text editor. I use flo's notepad 2, but you could most certainly use notepad++, editPlus, gEdit, textWrangler, win32pad, and so forth. You take your content or a reasonable facsimile of future content, and you put it into a 'logical document order' as if HTML didn't even exist. The ONLY reason to be working in a paint program at this point is for CONTENT images. Then you mark that content up semantically, saying what things ARE, NOT what they look like. If at this stage you choose your tags based on their default appearance you are choosing the wrong tags for all the wrong reasons. Then you bend that markup to your will with CSS for your various layoutS -- yes, PLURAL -- for all the media targets you want (screen, print, aural) to specifically target, as well as the different media queries -- adding any semantically neutral containers like DIV and SPAN as needed. Said designed layout should be elastic (fonts and any widths/paddings declared in EM's), semi-fluid (max-width so long lines aren't painful to read), AND responsive (using media queries to adjust the layout by width) -- ANYTHING else is inaccessible bull, don't let anyone tell you otherwise.
THEN and ONLY THEN do you have ANY business adding colors, borders, shadow effects, or going into your paint program to make non-content images (if any, thanks CSS3!)
It's called "progressive enhancement", starting with what's ACTUALLY important, (content), and progressively adding markup, css, presentational images, scripting so that should any of those be blocked/unavailable, the page "gracefully degrades". Content dictates markup | markup and content dictates layout | layout dictates sizes of graphical elements - THEN you can make it pretty.
Of course, my view on design is a bit heretical (I know, big shock) in that to me, good design is one I DON'T notice; I am far more likely to notice problems in a design than to be hit with 'wow' factor over how pretty something is. More so if the design distracts from or gets in the way of what I actually came to the site for -- CONTENT!
... and at the end of the day, that's what people go to websites for -- YOUR CONTENT! I don't care how pretty the result happens to be on the designers magical combination of screen size and font sizes, if it's an inaccessible mess for anyone who dares to need different font sizes, different screen sizes, zooming, or even (JHVH forbid) non screen targets -- what the hell good is it? (and to be frank, I've NEVER seen a page that was pissed out by a PSD jockey that was worth a flying purple fish on any of those counts!)
Which is why most of the artsy-fartsy fancy "design" PSD jockeys sit around circle-jerking each-other over is usually useless to the vast majority of visitors, and in most cases little more than dumping a can of shellac on a pile; no matter how much you polish it the result is still bug * on horse *.
Unfortunately though, it's become industry standard practice to polish that turd, since your typical "suit with a checkbook" doesn't know enough on the topic to make a rational informed opinion on having a website, and are far more easily swayed by a flashy picture than an actual presentation of substance. "Image is everything" no matter how badly it results in chopping oneself off at the knees in the long run.
In many ways it's just another manifestation of "Pay more later for something you can't afford now" that's one of the driving forces of the continued decline in world economy. It's an attitude that is little more than a cancer eating away at society.
Though -- when it DOES come time to add presentational images to a page -- like a logo -- any of the tools will usually do the job, I just like to have a really good save-time image optimizer so I don't have to go back with another program to re-optimize after save. That's why I like "Paint Shop Pro" -- I have the latest from Corel, but primarily I still use JASC version 7 because it's leaner, faster loading, and still does everything I need done. It still has one of the BEST save-time image optimizers (that they thankfully left in place in newer versions) around, the only thing I usually need to post-process for is stripping the GAMA line from PNG so IE doesn't try to color-correct it. I've actually been using one version or another of Paint Shop Pro since Adobe snatched up Aldus and buried Photostyler, which at the time was (and in many ways still is today) vastly superior to Photoshop... which would mean I've been using PSP since about the time Windows 95 came along with long filename support.
IF you are using Photoshop or some other Adobe program, get yourself a decent image optimizer like PNGCRUSH, or save as 24 bit PNG and then optimize in some other program (even if your result is going to be jpeg) because Adobe wouldn't know image format optimization from the hole in their.... DVD... yeah, DVD. That's the word I meant to use.