The important risk depend on the reason of proxy usage:
- Risks and hazards of proxies in general
- Risks and dangers of anonymizing proxies
Risks and hazards of proxies in general
If you use a proxy, then the whole network traffic runs over it. A proxy is thus in a position to take note of all what you receive and send.
That proxies can cache data, is one of its advantages. So sometimes they can respond faster and more directly, instead of retrieving the data from the remote server. Normally entirely unproblematic.
For secure connections (HTTPS), very dynamic content, and membership areas and customer areas, it is often instructed that these contents are not cached, neither in your browser’s cache, and certainly not in proxies. After all it os of no use, if you have to explicitly log into your member area, and information from this area can be found in proxy caches afterwards. The proxy must obey the request to not cache. Technically, it may as well ignore it.
Data you send can also be logged. This includes transferred unencrypted credentials (account, password).
Risks and dangers of anonymizing proxies
An nonymity service lives of the users‘ desire for privacy and offers it. This can be done technically only in the form that the service create no log files at all. Because only if there is no logfile, the service can not be ruled to disclose it.
Of course the use of an anonymity service does initially not mean, that the user has something unlawful in mind. Some users just dislike the data collection, even if this usually only used (and usable) for troubleshooting and statistical analysis for site optimization.
Other users do not even care about the anonymity itself, but want to request content, that is available in general, but not at their location. This mostly happens with video or music. The users use the anonymity service to hide their real location.
Of course, other people have sometimes „good reasons“ for use of these services, for example because they want to access questionable content.
If in this case the anonymizer collects data against all promises, one has no more and no less than if one had accessed directly. Depending on usage, this is annoying because one had used the service to no purpose and/or paid for it, or can lead to severe problems.
For security reasons you should only choose a well known commercial provider.