Anthropologies has a pretty unique aesthetic, which is why they're so successful. However, I think the most obvious source for similar style is Modcloth. Here are some options that offer the same playful, graphic look.
Any Which Way Dress
Aftershock Dress
Unexpected Twist Dress
If Modcloth doesn't offer what you're looking for, you should check out Ruche, a similar site with a slightly girlier feel.
If an almost endless selection doesn't scare you away, you should check out British retailer Asos, who just started shipping to the states. There is a huge array of prices points, from $50 to $500 among hundreds of dresses.
Forever Unique One Shoulder Dress (ok, not much cheaper than Anthro, but I liked it)
Next, you can head over to Shabby Apple for some vintage inspired options that sometimes have an Anthro-style quirk
Baja Dress
Champs Elysees Dress (Looks nothing like the inspiration, but I love it)
For more Anthro style dresses, check out Tulle, Topshop, and (sometimes) French Connection. Hopefully this was helpful!