Common words:
* Impart: to communicate or make known
* Impeach: to formally accuse a public official of misconduct
* Impel: to drive or urge forward
* Implement: to put into effect
* Imply: to suggest or indicate indirectly
* Import: to bring in from another country
* Impose: to force something onto someone
* Impossible: not possible
* Impress: to make a strong impression on someone
* Improve: to make better
* Impulse: a sudden strong feeling
* Impromptu: done without being planned
* Imprudent: unwise
* Impulsive: acting without thinking
* Impunity: exemption from punishment
* Impute: to attribute something to someone
Less common words:
* Impale: to pierce with a sharp object
* Impartial: fair and just
* Impassable: impossible to pass through
* Impeccable: flawless
* Impediment: an obstacle
* Impending: about to happen
* Imperative: essential
* Imperceptible: impossible to perceive
* Imperfect: not perfect
* Impervious: not allowing fluid to pass through
* Impetuous: acting quickly without thinking
* Implicate: to show involvement in something
* Implore: to beg earnestly
* Imply: to suggest or hint at
* Importunate: insistent
* Impotent: powerless
* Impound: to seize and hold
* Impregnable: impossible to capture
* Improbable: unlikely
* Improvident: lacking foresight
* Impudent: rude and disrespectful
* Impugn: to challenge as false
This is not an exhaustive list, but it gives you a good starting point.