Requesting administrator privileges at run time

Is it possible to get a C++ application running in Windows to request administrator privileges from the operating system at run time?

I know it can be done at compile time, but can't seem to find anywhere whether it can be done at run time.

Thanks for your help!

EDIT: What if I want the current instance to have elevated privileges? For example, I might have data stored in memory which I want to keep.

If you want the application to always elevate, you can give it a manifest, either by building one in (not compiling technically) or by putting an external manifest in the same folder as the exe. If you want to decide, as a person, to run it elevated, you right click the exe or short cut and choose Run As Administrator. If you are launching it from code, then as @vcsjones comments, you use the runas verb when you launch that process. For example:

ShellExecute( NULL, 
    "runas",  
    "c:\\windows\\notepad.exe",  
    " c:\\temp\\report.txt",     
    NULL,                        // default dir 
    SW_SHOWNORMAL  
); 

Not quite, but you can do the opposite—you can drop privileges if you already have them. So, you can have your program start out running as an Administrator, using one of the methods listed by Kate Gregory. Then, drop your unneeded privileges; see Dropping privileges in C++ on Windows for how to do that.