OpenStreetMap's processes are carefully designed to minimize the privacy footprint of the mappers.
Nonetheless, the principle that any edit shall be attributable means that some data is still recorded.
An overview is given which data is recorded at all and which of it gets available to whom.
OpenStreetMap surveys data about places, not about persons. Thus privacy sensitive data in the geodata is very rare and always unwanted. Likewise, the principle of distributing the data allows data consumers of the geodata to stay as anonymous as they want. Mappers can contribute with pseudonyms, although not completely anonymous.
However, for both the social features of OpenStreetMap and the purpose of attribution for the edited data it is necessary to collect some privacy related data. A useful starting point to see your own data footprint is the tool HDYC.
All the edits you make are grouped into changesets, and the editing software will urge you to add a comment per changeset. As both the edits and the changesets carry dates it is possible to track your activity times. The nature of some edits may suggest local knowledge thus that you actually have been at the mapped places. The kind of edited objects and the mapping standards can be checked by every other contributor as well. Most often, this is simply a reason to be proud of the achievements, but you should know and check before it might get a matter of concern. Using separated accounts for different mapping tasks is often an appropriate solution and well-accepted in the community.
OpenStreetMap offers additional ways to interact: you can leave comments on changesets and notes on the map, you can discuss on mailing lists or the forum, or you can answer questions on help.
You can write documentation on the wiki. All of these channels have their own rules with regard to how long the data is stored, how it is searchable, and whether you can hide or delete your contributions.
The talk presents the data traces of each channel and discusses strategies to get the desired degree of privacy.