In Drupal 7, not only do you have region.tpl.php in which there's ample opportunity to customize wrapper markup around blocks, you are also able to override block markup on a per-region basis via a block--REGION_NAME.tpl.php file, as well as alter any block variable based on $region within your THEME_NAME_preprocess_block() function.
For Drupal 8, while we will retain region.tpl.php or an equivalent way for customizing wrapper markup, we are proposing to remove per-region block markup customization from core. Based on discussion with various people, we believe such customization is generally not a good modern semantic practice, and that CSS 3 and Sass provide more appropriate tools for customizing how blocks look in different regions. Meanwhile, removing the flexibility makes it easier to reuse blocks in different display contexts.
If you have a Drupal 6 or 7 theme that relies on per-region block markup, or have a use case in mind where it's needed, please comment on the issue. It's possible that the use case can be solved in an alternate way, or it may be the case that we'll need to retain the flexibility or provide a contrib module that reintroduces it.
Thank you.
PS: There's also a related issue for removing zebra and counter variables from the template too, for similar reasons.