Well this got to be the GTD app with the best UI concept ever.
Actually I downloaded DayMap only because it was on sale, well, it looked interesting from screenshots and videos. I am a heavy OmniFocus user and didn't think I'd have much use for it. But now after trying, I find this app completely convincing, and ever since downloading I use it daily.
As Actwolf described below, it's a brilliant UI concept, look and feel. And it has to be mentioned, while DayMap follows minimalist principles, projects can go surprisingly "deep", splitting up tasks into sub-tasks, sub-sub-tasks, sub-sub-sub-tasks (etc. etc. etc.). Of course, DayMap is no OmniFocus, so if you need something really complex, DayMap isn't for you. But even then it might prove useful as a companion app: I use DayMap for one specific part of my work-life and for that it serves me very well.
DayMap has one killer feature for me: it shows recurring tasks in the calendar as multiple items, so for example you can have one task repeated from Tuesday to Friday and DayMap will show an entry for every day (Tuesday-Wednesday-Thursday-Friday). Other apps (like OmniFocus) generate the next (repeated action) only after the first one is completed.
This way, DayMapThis is ideal if you have tasks that take longer, and you want to work on a task every day a bit. So unlike the other to-do apps, you don't just get to see a frightening due date, but instead you see when you will work – more like with planing software. That is really great for motivation.
Regarding the feature requests of other commentators here: Personally, I wouldn't need these, and with every new feature the developer runs risk of ruining the clean interface. "All in one place" is usually a way to get things cluttered. I hope the developer goes here his/her own way and won't sacrifice UI for features. This is not to say that there isn't anything to improve with this app, I see quite a few things where the developer could work on – before adding new features.
Anyway, one more thing, it has to be said: at 13$ this really needs a demo version, and I find it rather mind-boggling that the developer doesn't provide one. DayMap is a well-done, polished app! I really have a hard time trying to understand that. Productivity is an individual thing, one has to be able to evaluate what works best for his/her needs. So, dear developer, it's very simple: if you don't want to offer a demo, you have to sell at 5$-8$. If you want to sell your app at 13$ you need to provide a demo. It is true, you can always find new customers by setting your app from time to time "on sale", but this is actually pretty unfair to those customers who payed full price.