Can I incorporate in USA if i'm not resident and not American?

I'm a foreign national, and resident in a different foreign country. I have no ties to USA, and no intention to hire any employees there.

Can I still register a company (e.g. C Corp)?

If it is possible and I do this via an agent in USA, how much will it likely cost?

[EDIT - I know there is likely a ton of other issues, like figuring out how to apportion income, dealing with tax, etc. but I'll deal with that bit later]

Yes!

• Step 1 - Get a mailing address: You can either lease a property or get a mail box (po box will not work). In the us corporations are handled on a per state basis. The state of DE is probably your best bet in regards to pricing, tax friendliness and corporate protection. I recommend getting a UPS store account. They can forward your physical mail anywhere in the mail. Here is one I use for my INCs which has the lowest rates in Delaware. http://www.theupsstorelocal.com/4755/
• Step 2 - You will need a registered agent. An RA is someone who can recieve corporate documents and law suits on your behalf. In essence its a physical person who the state can reach. Google Delaware registered agents. This costs around 100 to 200 usd per year.
• Step 3 - Fill out your incorporation documents for the state of DE. You can do these yourself and the state of DE actually has a sample you can grab from their site. All it needs is the business address and the registered agent. Type one up, and mail a check to DE department of corporations.
• De will send your corporate documents to your UPS store. Have them forward them to your location anywhere in the world
• The US IRS will require you to get an EIN for your corporation. This is done online and is free. Look up IRS S-4 application, fill it out online and print your new EIN number.
• Last step is to open a USA bank account. Since 9/11 its become next to impossible for a foreigner to open a bank account. Even though the account is opened under your corporation most banks are required to have a USA resident also sign off on things. You can get around this by nominating a CFO (someone you pay for their services) to go to a bank, open an account and forward you the documents. They will have access to your account, but professional accountants, CFO for hire, and even book-keepers have very little interest in getting arrested for robbing you. Just make sure you have an agreement which protects them of liability and you from theft.
• Make sure the bank you choose allows online transfers. Or somehow come up with a way to wire, paypal yourself the money. In most countries you can withdraw at an ATM or use a visa card the bank will give you that is linked to your business account.
• Yearly you will have to file corporate tax returns. They will show the profit the business made, minus any expenses. The amount left over is taxable. Talk to an accountant in the USA and one in your host country. Usually if you send off 100% of the net revenue to your own country then you have no USA tax liability. (the exception is if you are a USA citizen where you are taxed on your income regardless of where it is earned).
• You can open up an Merchant account (to accept credit cards) using your corporate information. I know Stripe.com allows this, and I think paypal also does not require a US social security number when you use an EIN / Corporation name.

The total costs you are looking at are around $500 per year plus any mail forwarding costs and whatever a book-keeper will charge you. Since you said you are in Hong Kong, check out East West Bank. They are a Chinese bank with a physical presence in the USA. They might be able to open an account for your without you having to go through the trouble of nominating a CFO. http://www.eastwestbank.com/English/index.asp

Incorporation rules are different based on location (state). Some states are more strict than others and a simple Google search on this will point you in the right direction. That said, as a general rule, you will need a registered agent to act as the official business address in the state where you wish to incorporate. There are many services that offer to act as registered agents for people from other states and countries wishing to incorporate in a different state from where they reside.

Incorporation can range from a couple hundred dollars to several thousand. Registered agent services can be found for as little as a $150 a year and go up from there.