Why am I posting this?
After googling this, the answers were very unclear, scattered and gave different answers. So, once I had worked out what this process was and what it does, I thought I'd help the world out and post a very clear answer here.
This Q/A covers the following:
What is Conime.exe?
Is it dangerous / malware?
Whilst this is a legitimate process, malware can (and does) use this name to help it go unnoticed on your system.
If you are unsure whether or not the Conime.exe that is running on your system is malware or not, you should scan it with an anti-malware program (it's good to scan with more than one, as no anti-malware program is perfect).
Some examples of anti-malware programs include (make sure they're up to date before scanning):
Can I remove it from the list of startup programs?
If you do not use Asian languages on your computer, you can disable this startup entry. Windows may re-enable it if it decides that you need it.
Can I remove it entirely?
As this is a system file, I would strongly advise not removing this file.
If the file has been shown to be malware, please use an anti-malware program to fix the problem as messing around with system files when you don't know what you're doing can break your computer (see above for a list of programs to try).
