What version of Windows are you on (XP, Vista, Windows 7, Windows 8 )? Is it 32-bit or 64-bit?
What is the version of Internet Explorer installed on your computer?
In Internet Explorer go to Help -> About Internet Explorer.
P.S. Please, don’t say that you are not using Internet Explorer. This is irrelevant. Skype depends on Internet Explorer.
Open Windows Event Viewer -> Custom Views -> Administrative Events. Look for the recent error messages with timestamp corresponding to Skype crash. Copy and paste here the text from the General tab.
Faulting application name: taskeng.exe, version: 6.1.7601.17514, time stamp: 0x4ce79d2c
Faulting module name: msvcrt.dll, version: 7.0.7601.17744, time stamp: 0x4eeb033f
Exception code: 0xc0000005
Fault offset: 0x00000000000027de
Faulting process id: 0x95c
Faulting application start time: 0x01cf4e65591bb060
Faulting application path: C:\Windows\system32\taskeng.exe
Faulting module path: C:\Windows\system32\msvcrt.dll
Report Id: a29b9b10-ba58-11e3-805e-0021979d31da
None of these error messages is directly related to Skype, but the problem might be with some of the system devices.
Please, run the DirectX diagnostics tool.
Go to Windows Start and in the Run box type dxdiag.exe and press the OK button. This will start the DirectX diagnostics program. Run this diagnostics and save the results to a file. Please, attach this file to your post.
Be aware that you will have to zip this file before attaching it here.