With which airline company do you need the lowest amount of miles to become a gold member?

"Gold member" is a very broad term and not every program uses it. Are you wanting to know about mid-level elite in an airline program or mid-level in an alliance?

Halothane

The first one that comes to mind is BD Diamond Club Gold (*A Gold) which can be retained for 38,000 miles...however, to get it in the first place you need to earn BD Blue+ (3k miles) and BD Silver (16k miles)

I believe Air Canada Aeroplan Elite (*A Gold) is in the 35,000 mile ballpark.

If your intention is to find the program that would be easiest for you to earn status, don't focus solely on BIS miles needed. Be sure to account for alternative EQM earning opportunities. For example, Delta and US Air offer the ability to earn status throuh multiple card-holderships alone. US Air has offered some aggressive promotions to use their partners and have purchases and other activities count towards your EQM total. American counts miles earned by any means towards "Lifetime Status", whereby earning a million or more miles will enable you to have automatically renewing status every year for the life of the program. Some airlines offer shortcuts to status if you can meet their challenge of a certain number of BIS miles in a limited period. The list goes on.

http://www.smarttravelasia.com/frequentflyer.htm

Frontier Airlines used to offer their first level Elite for 15,000 and top level for 25,000. It was also only 15,000 for a free R/T ticket. I am not sure if they still do this, its been about 3 years since I flew with them.

AA, because "Gold" is entry-level there.

At some other airlines, "Gold" is the second level up, which means you need a lot more miles.

Not only do status level names differ between airlines, but what you get with each level of status differs a lot. You need to explain much more, including the benefits you're after. The answer might be quite different depending on whether you want status mostly for upgrades, or mostly for lounge access, or mostly for access to preferred seating (eg, exit rows), or mostly for bonus mile earning on flights.

Also, are you interested in a worldwide answer, or is there a particular city you always start your travels from (which would restrict the airlines available to you)? You need to provide such info to get a practical answer.