You can do this without any external lib:
// Create image.
Image image1 = Image.FromFile("c:\\Photo1.jpg");
// Get a PropertyItem from image1. Because PropertyItem does not
// have public constructor, you first need to get existing PropertyItem
PropertyItem propItem = image1.GetPropertyItem(20624);
// Change the ID of the PropertyItem.
propItem.Id = 20625;
// Set the new PropertyItem for image1.
image1.SetPropertyItem(propItem);
// Save the image.
image1.Save("c:\\Photo1.jpg", ImageFormat.Jpg);
List of all possible PropertyItem ids (including exif) you can found here.
Update: Agreed, this method will re-encode image on save. But I have remembered another method, in WinXP SP2 and later there is new imaging components added - WIC, and you can use them to lossless write metadate - How-to: Re-encode a JPEG Image with Metadata.