“jucheck.exe” is part of the Java Runtime from Sun Corporation and not a trojan, IF it is located where it is supposed to be – usually something like “C:\Program Files\Java\jre1.5.0_10\bin\jucheck.exe“
Viruses or Trojans are normally named identically together with other program files and operating system components to avoid detection. If the files are in a location where they don’t belong then there is a good chance that it is a malicious file.
Some malware camouflage themselves as jucheck.exe, particularly if they are located in c:\windows or c:\windows\system32 folder. Thus check the jucheck.exe process on your pc whether it is pest and if this is the case then deleting it is recommended.