How do I create a category in Xcode 6 or higher?

They didn't forget. They just moved it without telling anyone.

1. Click File -> New -> File

2. Select Objective-C file under Sources in iOS or Mac OS respectively and Click Next

3. Now under File Type: choose either Category, Protocol, or Extension

PS. Under File Name: whatever you type here will be either the Category, Protocol, or Extension Name.

To create CategoryBaseClass+CategoryName.m/.h:

1. File → New → File... or use ⌘N.
2. Select Objective-C File.

3. Type in category name, select File Type: Category, and then select the base class.

4. Complete the flow to create the category.

Here's a visual demonstration:

Xcode6-Beta5 update

The interface has now changed and it's possible to add a Category directly from the New > File window.

See unmircea's answer.

I was surprised myself, and I guess because of Swift they forgot about good old Objective-C.

You have two options:

1. Create an Objective-C class with the category name, example UIView+Powerups, then manually change the interface to match the one of category. Note that the snippet for the category interface and implementation is still working, so that's extra easy: type @interface-category and @implementation-category.

2. Import it from Xcode 5! Use this command:

   cp -r /Applications/Xcode.app/Contents/Developer/Platforms/iPhoneOS.platform/Developer/Library/Xcode/Templates/File\ Templates/Cocoa\ Touch/Objective-C\ category.xctemplate /Applications/Xcode6-Beta.app/Contents/Developer/Platforms/iPhoneOS.platform/Developer/Library/Xcode/Templates/File\ Templates/Source/
   

   Close and reopen Xcode 6 and you'll find "Objective-C Category" in the wizard for the new file.