I'm am a huge fan of tea, and have found a few great places online. My usual criteria are a good selection of unflavored black teas and a decent selection of organic options. The below list is in order of my level of experience with them, not in order of most to least favorite, as they all have unique qualities that keep me coming back to each.
theteaspot.com: good selection of all varieties in both flavored and unflavored form. Their Shagadelic English Breakfast is one of my favorite English Breakfast teas.
arborteas.com: my recent favorite, also mentioned a couple of times above. A large variety of organic tea, and everything I've had is great quality. Love the Makaibari Estate Darjeeling (both first and second flush, each with its own great characteristics).
teavivre.com: Chinese teas are their go-to, and I like their selection of both green tea and black. I had a great keemun hao ya from here, and the dragonwell green is good as well. They also have a large selection of EU certified organic teas with the certification information scanned and available, something I haven't seen elsewhere. It is a French/Chinese joint venture I believe. When you buy from here your tea ships from mainland China.
adagio.com: this place has some weirdly named teas that can be confusing, but what I've had from here is good. Can't remember any one in particular that stood out.