Pretty much all cameras these days come with a USB cable, and this works pretty well. It's annoying that many cameras have proprietary connectors, but the mini-USB format is becoming more standard. Typically cameras will come with driver software that must be installed on a computer used to download pictures. More friendly is mass-storage support, so that the camera just looks like an external drive and doesn't need a specific driver.
(Older cameras may have come with slow serial connections, and video cameras have traditionally used IEEE 1394 FireWire.)
Personally, I never use the cable, instead removing the memory card and using a card reader, which tends to be faster and more convenient. Many computers come with readers these days, and USB card readers are cheap and easily available. Even laptops may have builtin readers for some card types, or one can use PC Card adapters. This also avoids consuming camera battery power when travelling.
You can make prints yourself on a photo-quality inkjet printer. These have gotten very much better, and even a current "general purpose" inkjet printer will do reasonably well on glossy "photo" paper. A dedicated photo printer will do even better, and can do things like border-less prints. The online services mentioned previously do make true photographic prints. The price is about the same, though you have to wait for the mail.
An attractive solution these days is just to have your neighborhood photo-finisher do it, since many are now becoming equipped with digital-capable machinery. Recently, we just emailed our images to the store, and they printed them for us! My local store also has a computer available with digital card readers, so you can just transfer your selected images to their computer, and walk away with your card.
Long-term permanent storage is a tough question, and was one of my real concerns in deciding to get a digital camera. Typically the picture files end up on your computer's hard drive after downloading from the camera. If you delete them, either on purpose or accidentally, they're just gone. So if you're going to be taking pictures that you value over the long term, you need to think about it. Not just the usual backup issues of not losing them, but how you're going to organize them so that you can find a particular picture in a year, or ten years, or your grand-children will be able to... I recommend against the online services for storage, since they have a nasty tendency to go bankrupt or otherwise disappear, and will never give you enough (free) storage.
Some possible answers: burn CD-ROM copies, or keep "mirror" copies on at least two separate computers (ideally in separate buildings). I do the latter, keeping everything "online" on multiple hard drives, which seem to be getting bigger and cheaper at least fast enough to keep up with my space consumption (which is many GB/year!). This also avoids the secondary problem of keeping track of lots of CDs or DVDs. Do put pictures into folders with descriptive names. Always keep the originals from the camera intact, so do any cropping, balancing, etc. into a copy.
Copyright Richard Schooler, 2001-2008 firstname.lastname@example.org