I thought it would be nice to start a list of reputable seed vendors. Please feel free to list any of your favorites.
I've broken the list out into U.S. and EU sections, but some U.S. vendors may ship to EU countries, and some EU vendors may ship to the U.S.. If anyone has any good Asia-Pac vendors, I'll add a third section.
While I don't want to invite "name and shame" over bad experiences, I do want to call out one vendor that has earned a lot of notoriety.
Pepper Joe is one of the most popular seed vendors, largely due to having excellent search engine placement. However, the original owner sold it long ago, and pepper communities are FILLED with people who bought seeds from them only to have them grow into something completely different (typically common habaneros).
Sea Spring Seeds - these people have single handedly kick started development of super hots when they created Dorset Naga. A trully obsessed chilli heads, selling seeds since 1994, their selection is kind of limited, but the quality of their seeds is undisputed.
South Devon Chilli Farm - another long standing chilli farm. Their primary focus has always been chilli sauces and condiments, but they also sell a variety of seeds. Again - excellent quality!
Suttons - this is a very old horticultural establishment, almost as old as US :) They sell all kinds of seeds, seedlings and equipment, including chilli seeds. Their chilli selection is very limited, but they have some rare (in the UK) seeds.
Note that some of the vendors listed here are controversial. Certainly there are a couple that I listed where I personally would never buy from them, but that's more for personal/ethical reasons. They all, in my opinion, are vendors who will give you what you paid for (accounting for unstable varieties, cross pollination, and the occasional honest mistake) despite any other criticisms.
I especially like that he labels which seeds are open pollinated, which are isolated, and which varieties have not yet been stabilized. That kind of transparency is really important. Plus Justin has been an active member of the pepper community for many years, and gets some excellent varieties and crosses before they hit the general market.