Depending on what phone you've got, backing up your contacts, messages and pictures can either be really easy or a complete nightmare. Hopefully, you've got a phone that's relatively straightforward, but if not don't fear -- there's usually a solution if you're prepared to spend some quality time with your handset.
The first thing to try is using your phone's software, which might include a back-up utility. One of the problems with using back-up utilities, though, is that they tend to back up all your content into an own-brand format that can only be re-opened by another phone of the same brand.
If the back-up utility just doesn't do what you need it to then you're going to have to divide the back-up process into separate parts, starting with your contacts. There are several third-party SIM back-up programs that let you stick your SIM card into your PC via an adaptor and back up all your contacts.
Before you try to back up all your contacts off your SIM card, make sure that all of your contacts on your phone are copied on to it, otherwise you'll find that some of them will stay on the phone.
If there are too many contacts and you can't transfer them all on to the SIM card, do it in shifts, transferring the ones that do fit on to your PC, before clearing your SIM and repeating the process.
Alternatively, you can use a Web site like ZYB to back up all your contacts straight from your phone, but you will need a compatible phone, and it's done over a data connection so you might incur charges.
If none of these solutions work for you, unfortunately you'll have to resort to the old-fashioned pen and paper method.
Next up are your text messages, which are probably the hardest thing to back up, but there are a couple of ways to do it. The first is again to try a site like ZYB, which also provides a text back-up service -- you simply text your messages to a special number and they are then stored online.
The only problem with using ZYB is that the forwarded messages won't have the original sender's details or the time it was sent. But if you've backed up your contacts on ZYB then you can add the details for those text messages once you've logged into your account online.
If you don't want to use ZYB, you can always forward your messages to another phone and then back to yourself, but again you won't be able to see who sent it or when it was sent.
Finally, you mentioned wanting to back up your pictures. This should be fairly straightforward and can be done over a USB cable, infrared or Bluetooth. First off, install whatever CD your phone came with and try connecting your phone to your computer using a USB cable. You should then be able to access your media files.
If that doesn't work then try sending your pictures over infrared or Bluetooth to your PC, but keep in mind that this may take a long time. The other option is to transfer all your photos on to your phone's memory card, if it has one, and then take the memory card out and put it into a card reader that connects to your PC.