I would say a hesitant 'yes', depending on the 8 year-old. There is some violence, but most of it is done in a 'Bond' type of way ie stylised and nobody obviously suffering/no lingering shots of gore. Just the same as the other Bond films they were showing during the day on ITV pretty recently. The only exception to this is a bit where he makes a surface cut into himself to get some shrapnel out (it's relevant to the plot, honest!), but again the camera doesn't linger and you don't get to see much and it's all over very quickly.
There's a couple of snogging moments, and one scene where he's briefly in the shower with a woman, but it only shows their heads and again it's not really that different to the other Bond films (naked woman covered in gold anyone? And we watched that as kids).
M swears quite a lot. If you don't want your kid to hear swearing, you might not like that. But again, it isn't gratuitous and is mostly funny and after all they hear worse in the playground.
In the main though, it's a fine film in the escapist tradition that is Bond which I think would put it into the 'family viewing' category for those with slightly older children ie 7/8 or older. Apart from the ultimately quite minor points above, it's not much different to any of the other earlier ones - I mean, there's nothing dark or disturbing or sinister about it (compared to, to my mind, the latter Harry Potters for example).