Strangest thing. I can generate Tasks programmatically in an Apex Visualforce controller without any problem, but if I use the identical code in an Apex trigger, I get a strange behavior. The Task object is created but not assigned to the Contact until I assign a Task that same Contact from some other source, and then - poof - the previously created Task objects suddenly show up on the Contact's detail page.

Here's the code in the trigger (NOTE that I am using a hardcoded ID for the Contact):

// This method will create a task
public void createTask()
{
    Task t = new Task(WhoId = '003Z000000WzJOt',
                                  Type = 'General Task',
                                  Subject = 'Create task for contact',
                                  Description = 'Description');
    try {
        insert t;
    } catch (DmlException e) {
        ApexPages.addMessages(e);
    }
}

I hesitate to add the code in the Apex Visualforce controller, because it is almost identical. The only difference is the return value of the method (PageReference instead of void):

public PageReference createTask() {
    Task tmpTask;
    tmpTask = new Task(WhoId = '003Z000000WzJOt',
                                     Type = 'General Task',
                                     Subject = 'subject text',
                                     Description = 'Description');

    try { 

        insert tmpTask;
    } catch (DmlException e) {
        ApexPages.addMessages(e);
        System.assert(false); // assert that we should never get here
        return null;
    }
    return null;
}