In this digital age, we shoot a lot more pictures than we ever did before. There is no cost of film to make us hesitate to press the shutter button. If you keep all your photos, eventually you're going to outgrow the ability to keep track of your them using folders on your hard drive and you're going to need some kind of gallery or library software to help you manage your media.
While there are many professional and hobbyist applications that cost hundreds of dollars and have extensive features, you may be surprised to find the functionality available in several free applications. They are very similar, but with some reduced features. These programs allow you to group, name, and import your pictures into their system. They support basic editing, like cropping, red-eye correction, some basic sepia or monochrome effects, and usually some printing and online sharing options.
Picasa - Google's offering. Free, runs on Windows XP or Vista, or Linux. Very low system requirements. Integrates with Picasa Web albums for sharing. Version 3 is very fast. Supports plugin buttons to add integration with other sites like Facebook and Flickr. Has Blogger integration.
Windows Live Photo Gallery - This is similar to the "Photo Gallery" that ships with Vista, but has many more web features, so I recommend that you go ahead and install this one instead. Runs on XP or Vista. Integrates with Windows Live Spaces, Flickr, and other sites. Good editing features, and a pretty full featured import dialog that will seperate the files on your camera by the date taken. I use this one myself. It's a free download, Microsoft uses a unified installer for all their "Live" applications, but you can just tick the box for only Live Photo Gallery and install that.
iPhoto - Runs on Apple's OS X only. iPhoto is a very slick consumer photo management application. It's not free, as it's part of Apple's iLife suite of appliations, but iLife is included on every new Mac, so you should have some version installed if you own a Mac. You will have to buy a new copy of iLife to get the latest version when updates come out. iLife makes use of the same printing services as Aperture Books, so you can get very high quality books printed this way.
blueMarine - This is an open source project that runs on Windows, Linux, and OS X. It's not finished yet, but in beta testing. blueMarine is ready for evaluation, but not production use, so it's not 100% stable. It has a feature set rivaling the organization sections of many professional products. Right now it mainly works as a database and organizer, but will eventually have editing capabilities as well. I'd watch their website for updates. It's hard to explain all their features, but they have a nice video overview here.