I'm slightly past this as both DS are now in secondary, but I'll offer my words of wisdom with the benefit of hind-sight.
I really think that parents' and schools' attitudes can hugely affect the children; we were lucky enough that our school encouraged and supported the kids, told them that the tests were important but that they were to just do their best, gave them lots of toast (recognised that some are from homes where they wouldn't have had breakfast) and extra play time and chances to run off steam. The teachers and support staff were clearly working really hard to get the children prepared but not to heap stress on them - both mine (one more academic, one borderline ADHD so a dreamer and very active) seemed to take them in their stride and both did okay. They worried a bit and spoke about being nervous, but I do think children by Y6 need exposure to things they will encounter in the real world; we cannot keep them bubble wrapped and hope that society will suddenly become really quite nice and look after them and their feelings in to adulthood.
I stressed to them that they were to do their very best and whatever they achieved would be brilliant and we would be proud.
I think a lot of the stress problems on the children this year are from seeing their parents worrying and seeing reports in the media, which just exacerbates their nerves and can blow things right up.
I know that some children are far more sensitive and that the above is a generalisation, but I think if everybody was able to calm down about the whole shebang then the children would be far less stressed. At the end of the day, it's a test and as other PP have already said is really for the school not the children. When mine went up to secondary the teachers said they don't really take the SATS results in to consideration for streaming; they spend the first couple of weeks testing the children and forming their own conclusions on their abilities.
I fully understand all the comments about the tests being too hard and that they should be more targeted to individual levels, but if they have to just be one or two tests rather than tailored, then surely it's better to work to the highest common denominator rather than bring everyone down to the lowest level, or this will leave the brighter students unchallenged. In an ideal world, tailoring would be wonderful though, and the intuitive computer testing model would be a fantastic leap in enabling our children to gain confidence in their own abilities.