Get a list of weeks for a year - with dates

I think the code below complies with ISO 8601:

var jan1 = new DateTime(DateTime.Today.Year , 1, 1);
//beware different cultures, see other answers
var startOfFirstWeek = jan1.AddDays(1 - (int)(jan1.DayOfWeek));
var weeks=
    Enumerable
        .Range(0,54)
        .Select(i => new {
            weekStart = startOfFirstWeek.AddDays(i * 7)
        })
        .TakeWhile(x => x.weekStart.Year <= jan1.Year)
        .Select(x => new {
            x.weekStart,
            weekFinish=x.weekStart.AddDays(4)
        })
        .SkipWhile(x => x.weekFinish < jan1.AddDays(1) )
        .Select((x,i) => new {
            x.weekStart,
            x.weekFinish,
            weekNum=i+1
        });

Bear in mind, that week calculations are done differently in different cultures and there is not a bug if you see week number 53!

using System.Globalization;

CultureInfo cultInfo = CultureInfo.CurrentCulture;
int weekNumNow = cultInfo.Calendar.GetWeekOfYear(DateTime.Now,
                     cultInfo.DateTimeFormat.CalendarWeekRule,
                         cultInfo.DateTimeFormat.FirstDayOfWeek); 

Just updating what Spender put, because I wanted to make the output of your Datetimes more towards what you wanted.

DateTime jan1 = new DateTime(DateTime.Today.Year, 1, 1);
//beware different cultures, see other answers
DateTime startOfFirstWeek = jan1.AddDays(1 - (int)(jan1.DayOfWeek));
var weeks=
    Enumerable
        .Range(0,54)
        .Select(i => new {
            weekStart = startOfFirstWeek.AddDays(i * 7)
        })
        .TakeWhile(x => x.weekStart.Year <= jan1.Year)
        .Select(x => new {
            x.weekStart,
            weekFinish=x.weekStart.AddDays(4)
        })
        .SkipWhile(x => x.weekFinish.Year < jan1.Year)
        .Select((x,i) => new {
            WeekStart = x.weekStart.ToString("dddd, d, MMMM"),
            WeekFinish = x.weekFinish.ToString("dddd, d, MMMM"),
            weekNum=i+1
        });

The change to correct the formatting to what you wanted is in the last select of the anonymous object.