The move to fully ribbonize Outlook meant many of Outlook's options moved. The most obvious being the Tools, Options dialog. Options is now on the File tab. If you use this often, put it on the Quick Access Toolbar (QAT). Almost everything is under the File tab now, with some options accessible from buttons on the ribbons, including Navigation pane, Reading pane, and To-do bar settings (View ribbon)

Send and Receive has its own tab, plus its the first button on the QAT. You can initiate a Send/Receive using the F9 key or set Outlook to check for new mail more frequently that the default 30 min (8 - 10 min is recommended). This is set in Options, Advanced (Send and Receive is at the bottom of the first screen) or press Ctrl+Alt+S to open the Send and Receive dialog.

Import and Export are under Open & Export.  They are also accessible from the Options dialog, Advanced, Export.

Buttons on my QAT are Send/Receive, Undo, Options, Save as, Account Settings, Message Options, Print Preview. The first two are on the QAT by default - I should remove Send and Receive and Undo from the bar since I use F9 the few times I need to initiate a Send/Receive and Ctrl+Z to Undo.

Shortcuts for commands on the QAT are Alt+n, where n is the position on the QAT (ie, Options in Alt+3). For this reason, I do not recommend putting commands on the QAT if they have easy to remember keyboard shortcuts.

Mail Settings

Warn before permanently deleting Deleted items is now "Prompt for confirmation before permanently deleting items". It's at the bottom of the Advanced section, in the Other group.

Viewing internet mail headers was removed from the right click menu (of a selected message). Now you need to open the message and go to File tab, Info, Properties button. If you use it often, add the Message Options command to the QAT. As a bonus, you can then use an Alt+n shortcut to open the header dialog. Video Tutorial: Add Message Options Command to the QAT in Outlook

Calendar & Tasks

Contacts

The Contact field is hidden on forms. It can be made visible in Options, Contacts "Show Contacts linked to the current item"

The Autocomplete list setting is on the Mail tab, Send messages section. Here you can disable the "suggest names" feature or clear it.

Security settings

Many security settings are now in File, Options, Trust Center.

Junk mail settings are now per account, not per profile. To view Junk Email settings for a specific account, select a message from the account the choose Junk Mail > Options on the Home ribbon.