System apps randomly won't open/crash

Question

Since OS X Lion, some system apps (Preview, App Store, Terminal, Facetime, Quicktime) will randomly refuse to open. When I click on a file that by default opens up one of these programs, or when I click on these applications directly to open, they will open for a split second then immediately crash. Once this problem occurs, it never goes away until I reinstall OS X entirely. In the past year or so, I have had to reinstall Lion/Mavericks five times, which is incredibly frustrating.
Does anyone have a clue why this happens, and whether there are better solutions than completely reinstalling OS X?

Answer 1

Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Console in the icon grid.
Step 1
For this step, the title of the Console window should be All Messages. If it isn't, select
          SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen.
In the top right corner of the Console window, there's a search box labeled Filter. Initially the words "String Matching" are shown in that box. Enter the name of the crashed application or process. For example, if iTunes crashed, you would enter "iTunes" (without the quotes.)
Each message in the log begins with the date and time when it was entered. Select the messages from the time of the last crash, if any. Copy them to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.
☞ The log contains a vast amount of information, almost all of which is irrelevant to solving any particular problem. When posting a log extract, be selective. A few dozen lines are almost always more than enough.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
☞ Some private information, such as your name, may appear in the log. Anonymize before posting.
Step 2
In the Console window, select
          DIAGNOSTIC AND USAGE INFORMATION ▹ User Diagnostic Reports
(not Diagnostic and Usage Messages) from the log list on the left. There is a disclosure triangle to the left of the list item. If the triangle is pointing to the right, click it so that it points down. You'll see a list of crash reports. The name of each report starts with the name of the process, and ends with ".crash". Select the most recent report related to the process in question. The contents of the report will appear on the right. Use copy and paste to post the entire contents—the text, not a screenshot.
I know the report is long, maybe several hundred lines. Please post all of it anyway.
If you don't see any reports listed, but you know there was a crash, you may have chosen Diagnostic and Usage Messages from the log list. Choose DIAGNOSTIC AND USAGE INFORMATION instead.
In the interest of privacy, I suggest that, before posting, you edit out the “Anonymous UUID,” a long string of letters, numbers, and dashes in the header of the report, if it’s present (it may not be.)
Please don’t post other kinds of diagnostic report—they're very long and rarely helpful.