It's a pretty short list, and not that satisfying. Jeenwong (in the Riverfront Market--closes at 5 PM) is probably the best option. The same owners are planning to open a new place, Ubon Thai, on Justison St., but it's not operational yet.
There are some Thai dishes on the menu at Jasmine on 202--they're good, but very limited, and I have no idea if they do takeout. It's more of a sit-down place, with a sushi bar etc.
Bangkok House is also on N. Union St. in Wilmington, but in my 13 years here, I have never been moved to try it. Probably I was scarred by my one awful, vile meal at Pan Tai (up the street, and thankfully now closed).
I like Jeenwong a lot. On Wednesdays at the Rodney Square farmers market Sweet Basil (formerly in Chadds Ford) has a stand with curry dishes, lettuce wraps, etc. Pretty tasty stuff!
Bangkok House is decent, much better than the Pan Thai that travelmad remembers. Very inexpensive compared to Jasmine. We do both takeout and dine-in and always see a line-up of orders waiting to be picked up. They have a fairly large menu with all the usual curries and noodle dishes as well as some less known specialties. Pretty equivalent in quality to inexpensive Thai in major cities, so probably the best bet for what the OP is looking for.
Bangkok House Restaurant
104 N Union St, Wilmington, DE 19805
Bangkok House is our go-to place for Thai takeout. Same family as Jeenwong (and Tamarind on South Street in Philly), I believe. I will actually only get takeout from Bangkok House -- dining in is an exercise in patience that I'm not willing to endure (when there is a disclaimer on the menu that basically says 'expect to wait,' and you're expected to make it through a spicy meal on one small glass of water, that's a problem). But the take-out is always ready and waiting when we arrive.