Transfer from Hong Kong Airport
 

I will be arriving in Hong Kong in the beginning of February and staying at the Langham Place hotel in Mongkok, Kowloon. My preference is to arrange for a taxi (in advance). The hotel wants $650HKD (appr. $83 USD) which seems sort of expensive. If that is the going rate, then fine. If not, can somebody suggest a reputable company or person who I can make pre-arrangements with. I've pre-arranged transfers for the rest of my trip, but I just can't seem to get a handle on this one. Any help would be appreciated. Thanks,

Just take the train to Kowloon station and then either a taxi or a free bus if one serves your hotel.

By far the quickest way and probably the cheapest, I think the train is about HK$100 and a taxi from the station would not be more than another $100.

Because I will have a lot of luggage, I was hoping to be able to take a taxi from the airport. Any ideas?

Take a taxi from the airport. No need to use the hotel car. There is a taxi line, it's easy to use, much cheaper than the hotel car.

I would agree that taking a taxi from the airport is the easiest and cheapest of the car options, and in Hong Kong, quite simple as taxis are metered and the drivers speak English (for the most part). The Airport Express train is also quite easy, and from the station in Kowloon you can just take a taxi, but I would agree that if you have a lot of luggage it can be awkward, although you can roll the luggage carts onto the trains to unload your bags; but if you don’t mind paying for a car service, they are available. If you want to arrange a car service other than through your hotel, one which I can recommend is Park Lane see http://www.hongkonglimo.com/. I have used them for almost a decade and they are very reliable. I don’t think they would be much cheaper than going through your hotel, but check. Also see the website for Hong Kong airport at http://www.hongkongairport.com and then click on “Transport” “Hotel Coaches and Limousines” which will give some other car service companies (including Park Lane).
See

Take a taxi, and since there are more than one Langham hotels in Hong Kong, you should have the name of the hotel in Chinese, just in case the driver isn't 100% clear.

http://hongkong.langhamplacehotels.com/china/index.html

[Funny that it doesn't have a page in Traditional Chinese, the written language used by 95% of the population. ]