Top picks of English language databases: BAS, JSTOR, MLA, ProQuest, and LexisNexis. It really depends on what is the subject that you are researching.
Almost all Library databases can be accessed from off-campus. When you access from off campus, you will then be prompted for your KU online ID and password to authenticate yourself as an authorized user. If you find sources through Google or other search engines, you may not automatically get access to Library databases and resources.