Dropbox is a fantastic service. I use it regularly to sync files between my desktop and laptop. It does have other uses though, like sharing files with your friends and even hosting a website. While I would not recommend you host your main business website with a Public shared folder using Dropbox, using the service to host some images, like your websites favicon, has some advantages.
If you are using a service such as Blogger and want to add your own custom favicon you have several choices of where to host your favicon. You can upload it and host it on Google’s server, although last time I tried they did not accept the .ico format. That works until you want to change your favicon then you have to do it all over again including updating your code that points to your favicon.
You could host your favicon on an image hosting service, but then they might delete it at anytime. Again if you want to change your favicon you will be redoing all of the code.
Since Dropbox can host files that are publically accessable on the Internet you now have another option. Following the tips and tricks wiki to making your own website you can simple create a folder for your favicon, and copy your favicon into that folder. The advantage of hosting your favicon in your Dropbox public folder means you have more control over it. If you decide to change your favicon all you need to do is simply copy over your existing favicon and it will be replaced on your website. You don’t have to redo the code pointing to it, and you never have to worry about an image hosting service deleting it.
If you have not tried Dropbox, you really should give it a serious look. They offer 2gb of space for free, which is more than enough to share and sync files between computers.
They also have a great favicon if you are looking for some inspiration.