I have ordered plenty of import games over the years, but realize many people are unaware of where to buy Japanese and European games. I have done my best to compile a list of retailers and other sites that sell imports to foreigners.
This site is based out of Hong Kong and deals in games from all over Asia. They are very good on stocking new items and random things like game soundtracks. The prices are full Japanese retail and shipping can be expensive. They also stock older retro imports at very high prices. Play-Asia excels in having an easy to navigate site and great search tool. Just beware if you order from their site, shipping can take awhile.
Based in New York City, this site specializes in newer games and pre-orders. The shipping is cheaper and faster than Play-Asia, but their restocking times are longer. They have a few retro imports, and the prices seem heavily inflated. Their site is broken into two smaller sites; one for pre-orders and another for stocked items. This odd setup makes navigating NCSX a nightmare.
This site is based out of a Japanese retail store. It is one of the few stores that accepts foreign purchases by credit card. They specialize in new games, pre-orders, and toys. AmiAmi's coolest feature is the inclusion of the exclusive pre-order bonuses that usually stay in Japan. The site usually sells out of pre-order allocations very quickly, so if you want the cool Japanese bonus items, order early!
Games of Japan
This site is owned by Hit-Japan from eBay and is operated out of Japan. They offer new games and retro games. Their specialty is retro stock at affordable prices. You can also request an old game, and they will attempt to find it for you. I got Tryrush Deppy for $35 this way. The shipping takes awhile, so go with EMS if you order from Games of Japan. Highly recommended for fans of retro games, just be cautious of the expensive shipping.
This site is similar to Games of Japan. They specialize in retro imports and have cheap prices. The shipping is quicker than Games of Japan, but the EMS rule still applies. My one complaint for GameBaz is that they will allow you to order Out of Stock items without knowing it is Out of Stock. I purchased a game there, and it took them a full week to tell me they didn't even have it. I got a quick refund, but that is just bad business.
Amazon (Europe, Japan)
While technically you can't order games from other regions through Amazon, you can email the sellers to ask if they ship internationally. You can find some amazing deals on imports if you are just willing to email foreign sellers and pay a higher shipping fee. This is the most simple way to find European games like Tingle or Last Window for a reasonable price.
eBay, other auction sites
Auction sites can be a mixed bag. New imports usually sell for more than actual retail price, and pre-ordering through eBay is borderline retarded. You can get the occasional deal on some retro stuff, but most of the time a site like Games of Japan is better to use. The auction sites are great places to find rare games, just expect to pay full collector value if you do.
There are other sites like Gamebrink and JapanVideoGames, both of which I am unfamiliar with and know almost nothing about. If you have any suggestions I left out, feel free to place them in the comments section below.