That depends on why you need a bodyguard, anonymous. Almost any pokémon can serve as bodyguards for very specific reasons.
For example, most people employ fighting-types, as many fighting-types possess larger, more imposing forms or the hand-to-hand combat skills to discourage a physical assault from a human. Tyranitar, aggron, and vigoroth may also be used for similar purposes. (Slaking is not used for this purpose, however, as its special ability and generally lazy nature tend to make it a less-than-ideal candidate for such a job.) Aggron in particular tends to be extremely popular for this purpose.
However, assaults from a pokémon tend to be handled by either shedinja (which is protected by Wonderguard) or dark/ghost-types such as sableye or spiritomb. Spiritomb is especially favored for this job, as they also possess rather imposing statures themselves.
Other people use psychic pokémon for their bodyguards, thanks to a combination of their powerful telekinesis (which are effective against bullets and other weaponry) and their precognitive abilities (which are effective against, well, any situation). Psychics can also neutralize poison-types and protect their owners from telepathic assaults.
Then you have the people who prefer more discreet methods for a wide variety of reasons, including for use in highly public events. Members of the gastly line tend to be the most popular for these cases, as their abilities to turn themselves invisible and slip into and out of shadows make them very difficult to detect. However, any ghost-type with an intangible body (and thus, most ghost-types barring the shuppet line, shedinja, and the ghosts of Kalos) and smaller dark-types work just as well.
Of course, then you have the people who employ “cute” or “fluffy” pokémon such as clefable, wigglytuff, blissey, or audino as bodyguards, possibly because nothing guards a human being against the violence of our world better than irony, I suppose. Also, these four pokémon, when angered, are terrifying, and anything that could aim to hurt you will learn that rather quickly if they don’t already know.
Naturally, the above are only a list of commonly used bodyguards as far as I’m personally concerned. That is to say, these are the ones that I know about thanks to either personal experiences or connections who run security operations themselves. (No, readers, I was never on the wrong side of a bodyguard, contrary to popular belief. Newly established leagues have a tendency to hire bodyguards to look after me whenever I set up a storage system in a new region, especially after that rather nasty Team Plasma business.) The point is, there could very well be other types of bodyguards out there for scenarios I wouldn’t be able to dream up myself. Thus, the simplest answer is, possibly, to think of a scenario and then think of the best pokémon to counter that scenario. From what I understand thanks to the aforementioned contacts, that’s largely how security works.