Recently I've had a lot of friends that want to dip into the photography world, and after the inevitable "what camera do you have" discussion, and after they buy a fancy camera comes the Photoshop question. Do they need it, how much is it, do I use it, how do you use it... on and on. My response usually includes the phrase, "you don't need Photoshop to take great photos," which is true. I started taking photos long before I ever got my hands on Photoshop, long before I had a fancy camera. However, the answer to that question is, "yes, I use Photoshop .. for somethings." More than Photoshop, I use Lightroom. It's capabilities are all anyone would ever need at half the cost of Photoshop. The straight to the point answer from me would be - if you want to do extensive retouching, HDR processing, and compositing then spend the money for Photoshop. If you want to take beautiful pictures and have the ability to adjust things like exposure, saturation, and have the option for simple effects like split toning, then buy Lightroom and enjoy!
All that being said, if you're shooting jpeg and just want to be able to crop or apply a few effects try something free or cheap like Picasa, Gimp, iPhoto, or the web based Photoshop Express. Don't get bogged down by what equipment or software you need. Just go out and shoot!