How can you exclude files from being backed up?
Open System Preferences » Time Machine » Options. Here, add folders that you wish to exclude.
These folders will not be backed up to your Time Machine disk.
What should you exclude?
Concerning privacy, the following would be a starting point. Note that this heavily depends on how far you take the meaning of "privacy" and how important your data is to you.
~/Library/Keychains/ – this is where (probably) all your login data is saved. Examine it with Keychain Access.app.
~/Library/Application Support/Google/Chrome – this is your entire Google Chrome profile.
Generally, OS X apps should store any kind of login information in the Keychain. Not all need to comply with this, so you can't generalize this in any way. Don't trust your backup to be completely safe. OS X Lion can encrypt your Time Machine backup – this is only one tier of protection though.