Explicit joins should always be used; implicit joins have several problems:
The join condition is somewhere in the WHERE clause, mixed up with any other filter conditions. This makes it harder to see which tables are joined, and how.
Due to the above, there is a higher risk of mistakes, and it is more likely that they are found later.
In standard SQL, explicit joins are the only way to use outer joins:
SELECT d.Name, e.Fname || e.LName AS EmpName FROM Departments AS d LEFT JOIN Employees AS e ON d.ID = e.DepartmentID;
Explicit joins allow using the USING clause:
SELECT RecipeID, Recipes.Name, COUNT(*) AS NumberOfIngredients FROM Recipes LEFT JOIN Ingredients USING (RecipeID);
(This requires that both tables use the same column name.
USING automatically removes the duplicate column from the result, e.g., the join in this query returns a single