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It is not possible for someone from another computer to access your instant messages unless they have your personal username and password, and even in this case, it is most likely not possible.
Most instant messaging services have an auto save feature, where the system will automatically save conversations. The saved conversations are stored in a file that anyone using your computer may access. Your chat buddy may also have this as well.
You can turn off this feature by viewing the preferences file and finding the auto save feature.