I was going to write a side by side comparison between different softwares and analyze their advantages and disadvantages. Then it occurred to me that neither of us have time for this. I'll make it short and sweet, that is the whole point of this exercise.
First of all, why do you need a photo editing software? Because digital cameras suck at capturing reality, they suck even more than film cameras. Cameras cannot capture what our eyes can see, only an approximation, and even then it is sometimes off, by a bit, or by a mile. Almost every pro (or serious amateur) who shoots digital post-process their photos to some degree.
If you are serious about photography, then fork over several hundred dollars for Photoshop. There is not ifs or buts. Photoshop is the standard, nothing gets close to it.
It is also a big, sophisticated, complicated piece of software. I have been using it for years and I forget things at the same rate I learn new ones, but it is still worth every penny they charge for it.
If you cannot pay for the full version, or don't need it, there is also Photoshop Elements. It's easier, simpler, cheaper and if you never had any better then it's all you'll need. You'll still need to learn how to use it. It takes time and effort.
On the free side of the spectrum, I have used a lot of softwares, from GIMP to Picasa. If you would like to use Photoshop without having to pay, and are willing to put up with some clunkiness and stiffness, then download GIMP. GIMP is the closest to Photoshop available for free.
It doesn't matter which software you choose. If Photoshop were a car, then the rest would be different types of bicycles.
I may have found you a nice, fun bicycle though: it's called Pixlr, and it's an easy-to-use, pretty versatile free online program. You heard right: Free, our favorite four-letter F word.
Take this as an example. When I started taking pictures of this gift box I didn't noticed I had earlier set my camera for bracketing, this picture was a bit underexposed. You can see the steps I took (clockwise), it's similar to what I do to all my photos anyway (I shoot RAW, so there is always some post-processing).
I am seriously impressed by this software, and I am going to be using it in the future (I don't have Photoshop in my crummy laptop, and no way to get my photos usable when I am traveling). There is a lot more Pixlr does, and I found it really easy and intuitive, even fun.
The only big problem is that Pixlr does not work with RAW files. Curses! If you shoot RAW (if you camera can you absolutely should), and if your camera maker is as cheap as Nikon and did not include some decent software, then download Picasa to convert RAW files and work with Pixlr for files you'll use online.
Pixlrs also offers some ready-made effects, like the above (photo from the Pixlr blog). Nifty toy, I tell you.
And how about their wrinkled paper effect, and doodles brushes (image from the Pixlr blog), very cool for bloggers looking to spice up their graphics.
You have to give this a try, but be prepared to invest many hours learning how to improve your photos, but that is a given with whichever software you use. If the Pixlr project tanks, or stops being free, at least you'll learn things that can be used in Photoshop Elements as they are quite similar.
So, go to Pixlr, upload a photo from your computer and start playing. To learn a couple of tricks, for starters, go here.
Buy Photoshop CS5 at Amazon. Or download the (free 30-day) trial version.
Buy Photoshop Elements at Amazon. Or download the (free 30-day) trial version.
Download Photoscape (Windows only), free here. I haven't used it, but have heard good things about it.
Download GIMP for free from here.
Download Picasa from here (Mac, and Windows)
Use Pixlr online for free.
Use Photoshop Express online, here (it sucks, but it's free).
Use Fotoflexer (free, with annoying ads)
Use Picnik online for free, or with your Flickr account (decent editor, not as good as Pixlr).