First off, let me apologize for the site’s horrid layout. Do to upgrading, I had to pick one of the out-of-the-box WordPress themes. Hopefully I’ll have something a bit better up in the next day or so.
As mentioned, I just did upgrade WordPress, from 2.5.x to 3.7.1. Since you’re reading this, there’s a good chance that you also were doing something similar. If this is the case, and you haven’t already done so, I would suggest reading Upgrading WordPress – Extended Instructions over at Codex.
Now, if you have followed those instructions already, or have done something similar, you may have came across an error that said "Call to undefined function: wp_remote_post()" in either the update.php or cron.php files.
Have you tried disabling all of your Word Press plugins before doing the upgrade? From what I’ve read, this seems to fix it most of the time. If you have, I suggest that you rename the plugins folder by adding an "x" or any other way you’d like, and/or renaming eat of the folders inside, as well as the files that are in their (not the files in each directory, just the files directly within "plugins").
Now, if you’ve done this, and receive an error that says "Call to undefined function require_wp_db()" in wp-settings.php, then backup your existing wp-settings.php file (the instructions from above say to not delete it, unless I missed a step), and copy the newer version over and try again. If it works, then compare the two files, check to see if there are custom settings in it, and make changes.