To visit another country from Ethiopia, most countries would require a valid visa which they must have issued before you are allowed in however, there are a lot of countries you can travel to without visa so long as you have Ethiopian passport.
Most of these countries would grant you access without visa or they would issue visa on entry which can be valid for a specified number of days.
Such a length of stay is given based on policy revolving around the reason for your travel and in some cases, it would be determined by the immigration officer and there could be the option of extension when you run out of time. Below is a list of countries that would allow you access without visa but only your Ethiopian passport but make sure that you check with the embassy or consular office of the country you are intending to travel to very close to the time of your travel because visa policy changes every now and then.
Countries where visa is not required for Ethiopian citizens:
Saint Vincent and the Grenadines
There are more exciting countries Ethiopians can travel to without visa on the next page