Step 1: Identify the type of conditional sentence.
"If I ______ rich, I would travel the world" imagines a situation that is not currently true (I am not actually rich); this is a Second Conditional sentence, used for hypothetical or wishful situations in the present.
Step 2: Apply the Second Conditional grammar rule.
The structure is: If + Past Subjunctive, would + base verb; in formal grammar, the Past Subjunctive of "to be" for ALL persons is "were," not "was."
Step 3: Eliminate wrong options and confirm.
"Am" is simple present (not hypothetical); "Was" is colloquial but grammatically incorrect in the subjunctive; "Be" is the base form and does not fit here; "Were" is the correct subjunctive choice.
\[ \boxed{\text{were}} \]