Dump pictures from your camera and phone regularly. Once a week is a great goal, but if it's a busy season (a vacation or the holidays, for example), download them even more often. This helps keep them organized, but it also prevents them from being lost completely. The odds that your camera or phone will be broken or lost are much higher than that of your computer.
The easiest way for me to download photos is to plug in my phone or camera card to the computer, and just drag and drop into my photo organization tool (currently iPhoto). If you really don't think you're up to the regular task, then install an app like Dropbox on your phone that automatically saves the photos from your camera roll to a folder in the cloud that you can retrieve at a later time.
Cull. You really, truly, honestly do not need 16 shots of your toddler in the same pose in the same cute outfit. You don't even need six. You only need one, possibly two. When I download my latest photos, I immediately go through and delete all the extras. It's easy to trash the obvious blurry shots, but take another minute and choose the best of the ones that are similar, then delete the rest. Most of the time, I do no other touchups or color corrections or crops in the first pass. I just organize and delete.
Organize loosely. The key to organizing such large batches of photos is not to be so specific that it's time consuming. I organize loosely: September 2012 or Christmas 2010, for example. It narrows the time frame enough that I could find something later, but it's vague enough that I can always add pictures to it and not change my structure. The important thing is to find a way that makes sense to your brain. Adopting someone else's confusing way of organizing is helpful to no one.
Backup. I cannot stress how important it is to backup your precious family photos. I backup to a hard drive and also use the online service Carbonite. As a third measure, I print hard copies of the best photographs and keep them in photo boxes. These days, the printing step isn't necessary, but it forces me to mail pictures to the grandparents.
It seems like a lot of work, but once you're in a regular groove it doesn't take long at all. If you're already way behind, just start where you are. There's no need to start by organizing 10 years worth of pictures in order to move forward. Start with the photos on your camera and phone right now.
Getting overwhelmed with the amount of photographs we take can lead to documentation paralysis and make us not want to take any more pictures at all. But you'll regret it if you stop taking pictures or stop organizing them in a way that makes sense. As important as it is to capture the memory, it's just as important to keep it.