The SD card slot on my HTC Dezire Z is broken and a replacement is not available. How can I use my camera without an SD Card? I am using ICS.
You need a device with both internal and external memory. If your device have two different mounting points, then you have internal memory. One is for your (now damaged) SD slot, and the other is for the internal memory. Folder names shoul be /mnt/sdcard and /mnt/extsd (actual names may vary depending on the device).
You have two options:
Change the default storage for your pics. On Android 4.0, open your camera app, click on the "options" icon, there are 3 options, exposure / balance / settings, the first setting is "local storage", turn it on
Use a new camera app with options on where to save the photos you take. I love camera360 because of its amazing filters, and you can shoose where to save the photos
Another potential solution is to go external... There was recently a successful social funding campaign for MicroSD card readers that connect to the microUSB port of Android phones. http://www.meenova.com/