Sometimes I wonder why OmniFocus doesn’t do the obvious. For example, if I have a project with a task that is due today, why doesn’t that task automatically appear in the default Today project? Also, if there’s a Today project, why not also have an “Overdue” project that contains a lists of all tasks (and their projects) that are overdue? You could even take it a step further and have a default “Future” project that contains a list of all tasks (and their projects) that are due in the future.
Just my $.02.
OmniFocus 2 never had a default Today perspective. You’d have to create one. If you visit the Forecast perspective, you will find tasks that are due today if you have a task project with a due date assigned to it.
If you have OmniFocus 2 with the Pro upgrade, you can create a “Due” perspective that is grouped by Project and sorted by Due date to get any overdue and due today projects.
The Forecast view not only, as @wilsonng points out, shows tasks that are due today. It also, as you asked for, shows all tasks that are due in the future. It does not show the tasks’ projects, but it does show the project every task belongs to, which hopefully would be what’s interesting. You could even choose a certain period to show due tasks from in the Forecast calender. To me, the Forecast is a quite elegant solution.