My Mum died back in August. She specified in her will - made several years ago before dementia took hold of her - that she wanted cremation, a recyclable coffin and absolutely no religious content in the funeral whatsoever, and that's exactly what we did. The service was very short as a result - about 15 minutes. A few of us gathered - about 12 - the secular chaplain said a few words and gave us some time for quiet reflection, and then did the committal and it was all over in a flash. Since Mum hated to be the centre of attention, I think she would have approved.
One thing we did stumble over was the flowers. She had specified no flowers, but my Dad, in his 80s and quite traditional, couldn't bear the idea that people might think he hadn't bothered to make the effort to buy flowers for his wife's coffin and over the course of the week that thought began to really upset him. So we did go against her will on that and we selected a very simple spray for the top in a colour she would have liked, and how we did it was I paid for them so that he wouldn't feel he was going against her will. What we did was told everyone else no flowers, and asked for donations to the Alzheimer's Society in lieu, which a very common thing to do here. We thought that was a good compromise, and all the people who attended were close friends who were happy to go along with that. After the funeral was over, we had the flowers put into bunches and sent down to the care home where she lived for the last 3 years of her life, to brighten the place up (they were simple flowers and not at all "funeral-y").
We also didn't know what to do with the ashes, since she hadn't specified her wishes in that area. Dad didn't want them back - he thought it was macabre to have someone sitting in a pot on the mantlepiece, and I don't think he's quite ready to scatter, because that means saying goodbye. So for now her ashes are still at the funeral director's while we decide what to do with her, which sounds a bit grim but I think it would have tickled her, actually.
I think had she specified no funeral at all, we probably would have done just that. Neither of us really wanted to have to go - we were absolutely dreading it - Dad was worried about making a fool of himself breaking down in front of people and I didn't find that it gave me any closure at all. It was just a hideous, awful experience that I would rather have not had to go through. Plus, we had already said goodbye years ago, really, such is the nature of Alzheimer's. Had she specified that not having one was her wish, we probably would have honoured it for those reasons alone, I think.