Jucheck.exe is a process which checks for the available updates on the internet for your Java Virtual Machine. Jucheck.exe is a Java Update Checker. It is not a spyware, or malware. It is safe to your system. For more information about jucheck.exe, refer the below two links:
jucheck.exe - What is jucheck.exe?
jucheck.exe - jucheck, Java Update Check Information!
If you want to remove it, then follow the steps given in the below article:
How to Remove jucheck.exe?