The Block languages module, part of the Internationalization (i18n) package, allows you to configure for which languages each block is visible. The settings for visibility per language are provided under Visibility Settings via the Languages tab when configuring a block.
The Languages tab also provides a setting for whether the block is translatable. For custom blocks, the block title and block content will be translatable. For blocks defined by modules, only the block title will be translatable. If Make this block translatable is selected, a Translate tab will appear for that block. This tab provides a UI for adding translations of the block in each available language.
Don't forget to allow your used string format to be translated on admin/config/regional/i18n/strings or you are going to have a error message like The string blocks:block:1:body for textgroup blocks is not allowed for translation because of its text format.
Conflicts with Context
The Block languages module conflicts with the Context module, which alters how blocks are rendered. This issue can be tracked in the Internationalization issue queue: http://drupal.org/node/1343044