Cometdocs.com is a highly-regarded online document converter that has served over 3 million customers. All the conversions are web-based and completely secure, while guaranteeing the privacy. Your conversion needs are not shared with anyone. And above all, Cometdocs is without charge. You can use their conversion and transfer options for free, but for gaining access to other functionalities like hosting, sharing and increasing your limit on transfers and conversions, you will have to register on their website.
The only restriction, however, is the maximum file size for conversion. This is set on 30MB for the free plan.
Some examples of conversions you are able to do on Cometdocs.com: