Executing method every hour on the hour

If you want your code to be executed every 60 minutes:

aTimer = new System.Timers.Timer(60 * 60 * 1000); //one hour in milliseconds
aTimer.Elapsed += new ElapsedEventHandler(OnTimedEvent);
aTimer.Start();
private static void OnTimedEvent(object source, ElapsedEventArgs e)
{
    //Do the stuff you want to be done every hour;
}

if you want your code to be executed every hour (i.e. 1:00, 2:00, 3:00) you can create a timer with some small interval (let's say a second, depends on precision you need) and inside that timer event check if an hour has passed

aTimer = new System.Timers.Timer(1000); //One second, (use less to add precision, use more to consume less processor time
int lastHour = DateTime.Now.Hour;
aTimer.Elapsed += new ElapsedEventHandler(OnTimedEvent);
aTimer.Start();
private static void OnTimedEvent(object source, ElapsedEventArgs e)
{
    if(lastHour < DateTime.Now.Hour || (lastHour == 23 && DateTime.Now.Hour == 0))
     {
           lastHour = DateTime.Now.Hour;
           YourImportantMethod(); // Call The method with your important staff..
     }

}

Just a small comment based on /Anarion's solution that I couldn't fit into a comment.

you can create a timer with some small interval (let's say a second, depends on precision you need)

You don't need it to go with any precision at all, you're thinking "how do I check this hour is the hour I want to fire". You could alternatively think "How do I check the next hour is the hour I want to fire" - once you think like that you realise you don't need any precision at all, just tick once an hour, and set a thread for the next hour. If you tick once an hour you know you'll be at some point before the next hour.

Dim dueTime As New DateTime(Date.Today.Year, Date.Today.Month, Date.Today.Day, DateTime.Now.Hour + 1, 0, 0)
Dim timeRemaining As TimeSpan = dueTime.Subtract(DateTime.Now)

t = New System.Threading.Timer(New System.Threading.TimerCallback(AddressOf Method), Nothing, CType(timeRemaining.TotalMilliseconds, Integer), System.Threading.Timeout.Infinite)

I agree with Señor Salt that the chron job should be the first choice. However, the OP asked for every hour on the hour from c#. To do that, I set up the first timed event to fire on the hour:

int MilliSecondsLeftTilTheHour()
{
    int interval;

    int minutesRemaining = 59 - DateTime.Now.Minute;
    int secondsRemaining = 59 - DateTime.Now.Second;
    interval = ((minutesRemaining * 60) + secondsRemaining) * 1000;

    // If we happen to be exactly on the hour...
    if (interval == 0)
    {
        interval = 60 * 60 * 1000;
    }
    return interval;
}

Timer timer = new Timer();
timer.Tick += timer_Tick;
timer.Enabled = true;
timer.Interval = MilliSecondsLeftTilTheHour();

The problem now is that if the above timer.Interval happens to be 45 minutes and 32 seconds, then the timer will continue firing every 45:32 not just the first time. So, inside the timer_Tick method, you have to readjust the timer.Interval to one hour.

 void timer_Tick(object sender, EventArgs e)
 {
     // The Interval could be hard wired here to  60 * 60 * 1000 but on clock 
     // resets and if the job ever goes longer than an hour, why not
     // recalculate once an hour to get back on track.
     timer.Interval = MilliSecondsLeftTilTheHour();
     DoYourThing();
 }