Can you reproduce the problem?

This is important because a reproducible test case is often essential for debugging really hard problems. By reproducing the problem, the service provider can build kernels with special instrumentation to trigger, diagnose, and fix the bug. 

Are you using any third-party drivers?

Drivers run in the same address space as the kernel, with all the same privileges, so they can cause system crashes if they have bugs. 

What was the system doing just before it crashed?

If the system was doing anything unusual like running a new stress test or experiencing higher-than-usual load, that might have led to the crash. 

Were there any unusual console messages right before the crash?

Sometimes the system will show signs of distress before it actually crashes; this information is often useful. 

Did you add any tuning parameters to the /etc/system file?

Sometimes tuning parameters, such as increasing shared memory segments so that the system tries to allocate more than it has, can cause the system to crash. 

Did the problem start recently?

If so, did the onset of problems coincide with any changes to the system, for example, new drivers, new software, different workload, CPU upgrade, or a memory upgrade.