After Ma.gnolia Major Data Loss in 2009, I believe only Google, Microsoft and Yahoo services. Can I trust DropBox as my resource host? I would like to use my website's static content in DropBox and use it in my website. Is it good for me?
I would ask the question: can you trust your web host? I think unless you host your own servers on your own net connection (which you can't since it probably comes from some kind of telco company) etc etc.
You just have to trust them.
I don't know what their SLA is like, but if you're really concerned, I suggest using something like Amazon's S3 service which does have an SLA. (It's work noting that dropbox use S3 to store your files)
What do you mean by 'trust'? I'll assume you're talking about data loss.
If you are talking about data backups and preventing loss of data, you need to take responsibility for backing up your data. You can count on the company you are paying to do their best, but you have no real idea what their best IS until the feces hits the fan, at which point it's a bit late to figure out that their backup strategy just doesn't work.
You MUST ALWAYS be responsible for your own data. You can certainly pay other vendors to help with the task of keeping it available, but if you don't have a copy where you have physical control of the copy, then you are COMPLETELY at the mercy of people who's only loyalty to you is $29.99 a month. And you need to keep in mind that $29.99 will only barely pay for someone to pick up the phone.
Can you trust Dropbox? Sure. You can trust them to try to keep your data safe. Especially if you have one of their paid plans - they like money and by keeping your data safe, you'll keep giving them money. But if that's your only off-site storage, then you have a problem, because you just can't tell how good they are.
I wouldn't use Dropbox to host content because it will stop serving the resource if it's used too much:
If you want to share images, I suggest you use something like imgur (with a paid account). It's reliable and fast.
For other types of content, Amazon S3 can help you if you serve a lot of content.