It's the sap that's the problem with Euphorbia (and many other plants, incidently), so you need to take care if pruning. Otherwise it's fine. I've certainly had no issues with mine.

I've had euphorbia in two gardens and neither dog or cat has had problems. I think they know to keep away but in any case, as Rosierose said, it's the sap that's the problem. If you don't cut the stems there's nothing to worry about.

Its not likely to break by just being brushed up against - the stems are quite strong.

Thanks for your replies,that explains it. Ill definitely keep it then.