Arms are the most frequently tattooed part of the body. This common practice and choice has its roots both in Eastern and Western traditions and makes sense when you consider that our arms are very visible parts of our body and naturally lend themselves to being viewed in most situations.
Most frequently, we see that tattoo arm designs fall into two major categories, Japanese and American Traditional. These will frequently be naval or sailing tattoos, kitch Americana such as pin-up girls from the 40's and 50's style, flags, etc.. They are generally executed within a few basic styles, including different locations on the arm, different sizes, shapes and of course designs.
The idea is that the tattoo is dense enough so that no bare skin is evident and the appearance is as if you were wearing an article. You can even find some tattoo 'sleeves" to actually wear that way on e-Bay though I don't recall seeing anyone wearing one myself J.
Your choice is your own, of course, but taking into consideration your build type in general and the size of your arms in relation to the rest of your body is something that would be wise to consider before applying the ink.
Wrist tattoos are also gaining in popularity, especially with women who enjoy the "bracelet" designs of Japanese, Amerind or Polynesian origin to name just a few. Many of these tattoo arm designs are frequently of the "Tribal" variety and have special meanings to their owners and are believed by many to have some charm effect for them.
Men frequently will choose these tribal patterns because of their starkness and bold coloration. Be sure to consider the cultural and stylistic aspects of any tattoo arm design you choose. Many tribal designs have been "modernized" for contemporary tattoo art and are quite extraordinary.
Other wrist tattoos have designed flame bracelets and the flames will extend various distances up towards the forearm from the wrist area. This style tends to be more associated with the "biker" look and relates well to contemporary Harley Davidson flame paint jobs, to name just one association.
Once you decide on your design for any of these styles, you will need to locate a reputable, experienced and hopefully talented artist to entrust your precious skin to. Be prepared to pay for these because they require a lot of work and time.