Blockchain.info is a secure wallet to store your bitcoins, i have been using it for years since i was a newbie and didnt encounter any issues.
It has several features, private keys control and mobile app for our convenience.
They might have some bugs from time to time but it's only happening occasionally. I consider them as a very trusted web wallet but still don't be too confident with them when you are holding too much bitcoin. You never experienced any problem and issues with them, well that's rare for me as most of the people here experienced the same bugs. But when it comes to convenience, I like them and they have a very friendly support where you can asked anything when your problem isn't on the FAQs.