Martial Arts to compliment Hapkido?

Wrestling

Boxing

They would compliment Hapkido very well.

Well it depends on what you're looking for. BJJ, Judo, or Sambo would give you a well-rounded, strong grappling game. You might also consider supplementing with a striking art too. Boxing, Tae Kwon Do (common), Muay Thai. I specifically recommend the latter, but mainly because Hapkido and Muay Thai is similar to Kyuktooki (Korean kickboxing). lol

What are you wanting? If you want more something with similar style and an emphasis on the standing game, I would suggest checking out;

Silat (this has a lot of takedowns too)

Kali/Escrima/Arnis

Sanda (also a good amount of takedowns.)

Escrima and Silat would probably pretty easy to transition into from Hapkido.

If you want to be more rounded try checking out

Brazilian Jiu-jistu

Sambo

Judo

Hope this helps a bit.

I would focus on another discipline that puts emphasis on striking since you'll be able to incorporate that into your Hapkido training. just check yur local phonebook for schools that focus on the kicking and punching techniques, that should help you balance out the throwing and joint locking techniques of Hapkido. I myself first studied Tang Soo Do and transitioned into Hapkido later, and found it quite easy to incorporate one into the other. the main thing you want to focus on now is improving your "hard" side, meaning you want to learn a discipline that focuses on striking techniques (kicks, punches, elbows, and knees etc.) perhaps Muay Thai since it's such a basic and easy to pick up discipline and you could easily be incorporated with the Hapkido later (if there's a Muay Thai class near you of course)

I like what Ray said, boxing and wrestling. But whatever is your base style, stick to that and master it before moving on. If someone is not a Shodan or higher, you should not even consider another style. Unless, of course, you've move to a place that doesn't teach that style or you just plain don't like it. What I like about wrestling and boxing is that it is easy to incorporate into any style. So there is no harm in studying it. In other words it doesn't up root or changes the philosophy of whatever style you are studying.

Wing chun

Tai chi chuan

Escrima/arnis

Pencak silat

tkd traditionally compliments it.

I suggest SAMBO.