“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.
Non-system processes like jucheck.exe originate from software you installed on your system. Since most applications store data on your hard disk and in your system's registry, it is likely that your computer has suffered fragmentation and accumulated invalid entries which can affect your PC's performance.

In Windows Task Manager, you can see what CPU, memory, disk and network utilization is causing the Sun Java UpdateChecker Module process. To access the Task Manager, hold down the Ctrl + Shift + Esc keys at the same time. These three buttons are located on the far left of your keyboard.

This process is considered safe. It is unlikely to pose any harm to your system.

This process is not considered CPU intensive. However, running too many processes on your system may affect your PC’s performance. To reduce system overload, you can use the Microsoft System Configuration Utility (MSConfig) or the Windows Task Manager to manually find and disable processes that launch upon start-up.

Use the Windows Resource Monitor to find out which processes and applications write/read the most on the hard drive, send the most data to the Internet, or use the most memory. To access the Resource Monitor, press the key combination Windows key + R and then enter 'resmon'.