I have seen, and of course heard, literally hundreds of wedding speeches now, and they are always such a fantastic part of the day, from both a photographers and a guests perspective. Traditionally, the speeches would be held after the wedding breakfast, but more frequently couples are choosing to have the speeches at a different time. Sometimes, having the speeches before the wedding breakfast is a great idea if any of the speakers are nervous, and this means that all speakers can enjoy their meal fully, without worrying about standing up and addressing the room. I have known the speeches to be divided into segments, so maybe a nervous best man might speak before the meal is served and the others will follow after dinner, or sometimes the bride addresses the room shortly after the couple has sat down at the top table.
A particularly poignant moment happened once when a couple were presented with a card containing love and best wishes from an elderly grandpa who had passed away, and I can honestly say that the whole room was in tears. One maid of honour performed a rap for the bride, I have seen guests singing to the couple, a little flower girl performing a handwritten poem, and props from the best man including a full sized mouse suit, a tankini, car keys and frilly knickers!
Some couples choose not to have formal speeches, and just have an informal toast; either in the wedding breakfast room or sometimes in the bar or garden of their venue. As with every other part of your day, it is completely your decision to either stick with tradition, completely do your own thing, or, take the traditional elements and give them a twist of your own.