General:
* intercede: To act as a mediator, to intervene.
* interchange: To exchange, to substitute one thing for another.
* interconnect: To connect things together.
* interdependent: Depending on each other.
* interfere: To get in the way of something.
* interior: The inside of something.
* interpret: To explain the meaning of something.
* intersect: To cross or meet at a point.
* interval: A space of time between events.
* interview: To ask someone questions, usually for a job or article.
* intervene: To get involved in a situation to try to stop something bad from happening.
Specific:
* interbank: Between banks.
* intercollegiate: Between colleges.
* intercontinental: Between continents.
* interfaith: Between different religions.
* intergalactic: Between galaxies.
* intergovernmental: Between governments.
* international: Between nations.
* interpersonal: Between people.
* interracial: Between races.
More obscure:
* intercalate: To insert something into a series.
* intercranial: Inside the skull.
* interdigitate: To fit together like fingers.
* interlinear: Written between the lines of a text.
* interloper: Someone who intrudes on a place or activity.
This is not an exhaustive list, but it gives you a good idea of the range of words that use the prefix "inter-".