Stores and Shops

If you're just getting started, here's an excellent primer from our friends at This is Sternbild

Obviously, I can't list every retail outlet and supplier, but here are some that I have either purchased from myself or can somehow attest to their reliability

stores that ship internationally

General Merchandise
Hobby Search
AmiAmi
Hobby Link Japan
CDJapan
Otacute
Strapya World

Aftermarket, Doujin, Fan Made Goods
Mandarake
Rakuten Global Market
eBay (buy only from trusted sellers)

stores that do not ship internationally (must use a shopping service)

General Merchandise
Animate
Movic
Bandai Fashion Net
Amazon.co.jp

Aftermarket, Doujin, Fan Made Goods
Toranoana
Yahoo Japan Auctions

There are many different shopping services available for those that want to purchase fan made or exclusive items, do your research and find which one has the best rate and reliability for you.

US based stores
As retailers in the US catch on to T&B's popularity, they've started adding more items. Buying or preordering from these places have certain pros and cons. Shipping is usually cheaper and faster, but they take longer to receive stock and often have significant price markups (but also frequent sales and discounts). I suggest shopping around to make sure you're getting the best deal.
Big Bad Toy Store

For fun, here are some unofficial items worth picking up:
L'Eau par Kenzo, cologne for the discerning oyaji
Bunny apparently has relatives in Oregon that make fine wines at brookswine.com
Perplexitees has unofficial insignia T-Shirts
This tiger car is perfect for your Figuarts Tiger, and is still available at some of the above distributors as well as Amazon.com

As always, feel free to let me know any additions or corrections.