Do I need a computer to use a digital camera?

You don't, but your job of editing can get rather expensive if you have to print each image just to see if it will be usable.

Lets say you shoot 300 photos over a three month period and you print them all 4x6 inches on your printer at home. Paper and ink costs are around $.50 each print (photo labs run between $.18 to $.28 each) That would cost you around $150 at home and on the low end (from the lab at $.18 each) $54.

Since you obviously are using a computer to ask this question, I have to guess you are using a friends or are in a public library or something like that.

You can find deals on perfectly fine computers that cost under $500. There will be a program that comes with your "new" digital camera that will allow you to edit and make small corrections of the images you download to the computer. Over the course of time, the computer will pay for itself vs. making prints of every thing you shoot.

That is the printing part.

Now, what if you have some images you want to save as a file on a computer or all of them on a CD for future access? You will eventually have to format the card in the camera, thus loosing all your old images (don't depend upon using the delete button found on most cameras. That feature eventually causes the file index on the card to "loose" images)

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No, they make printers that you can plug your camera into or plus your removable memory card into. You can also go to some photo places and have then do it via your removable storage.

Essentially Yes. It will boost your digital photography 100 times.
Firstly, you will need to "dump" your images - those that you have taken - once it fills up your memory card/stick.

Secondly, with a PC and a freeware like Picasa 2 you can edit and make photos look better.

Thirdly, eventually you will end up with 1000s of photos/images, you will need a software to organize them.

Fourthly, you will end up printing 10 to 20% of all your images taken. So you still need a PC to store the rest.

Fifthly, you can create cool Screensavers, slideshows.....