In addition, the Academy allows the use of le as a singular direct object when referring to a male person (but not a thing). Thus "I see him" could correctly be translated as either "lo veo" or "le veo." Substituting le for lo is known as leísmo, and this recognized substitution is extremely common and even preferred in parts of Spain.
Other types of leísmo: While the Academy recognizes le as a singular direct object when referring to a male person, that isn't the only type of leísmo you may hear. While the use of les as a direct object when referring to multiple persons is less common, it also is frequently used and is listed as a regional variation in some grammar texts despite what the Academy may say. Thus you may hear "les veo" (I see them) when referring to males (or a mixed male/female group) even though the Academy would recognize only los veo.
Although less common than either of the above variations, in some regions le also can be used as a direct object instead of la to refer to females. Thus, "le veo" might be said for either "I see him" or "I see her." But in many other areas, such a construction might be misunderstood or create ambiguity, and you should probably avoid using it if you're learning Spanish.
In some areas, le may be used to denote respect when used as a direct object, especially when speaking to the person le refers to. Thus, one might say "quiero verle a usted" (I want to see you) but "quiero verlo a Roberto" (I want to see Robert), although -lo would technically be correct in both instances. In areas where le can substitute for lo (or even la), it frequently sounds more "personal" than the alternative.
Finally, in some literature and older texts, you may see le used to refer to an object, thus "le veo" for "I see it." Today, however, this usage is considered substandard.
Loísmo and laísmo: In some areas, parts of Central America and Colombia in particular, you may hear lo and la used as an indirect objects instead of le. However, this usage is frowned on elsewhere and is probably best not imitated by people learning Spanish.
A final note: The distinction between direct and indirect objects isn't quite the same in Spanish as it is in English, and thus the pronouns that represent them are sometimes called accusative and dative pronouns, respectively. Although a full listing of the differences between English and Spanish objects is beyond the scope of this article, it should be noted that some verbs use dative (indirect object) pronouns where the English would use a direct object.
One common such verb is gustar (to please). Thus we correctly say "le gusta el carro" (the car pleases him), even though the English translation uses a direct object. Such a usage of le is not a violation of the formal rules of Spanish or a true example of leísmo, but rather shows a different understanding of how some verbs function.
