Enable tab and shift + tab for code formatting

Though this is not a native StackExchange feature, there's a user script on StackApps that does exactly what you are looking for:

Better handling of indentation and the TAB key when editing posts

This user script changes the behavior of a few keys (most notably the Tab key) within the post editor to behave more like it does in IDEs or text editors:

• When multiple lines are selected, Tab and Shift-Tab indent and dedent these lines
• When nothing is selected, Tab and Shift-Tab insert or remove whitespace to align the cursor on a tab boundary
• When the cursor is within the left margin of a line, Backspace removes whitespace to align the cursor on a tab boundary (in other words, it may delete more than just one space character)
• On indented lines, the Home key toggles the cursor between the actual beginning of the line and the beginning of the real content (in other words, it jumps back and forth to before and after the leading whitespace). This only happens on lines that are indented by at least four spaces or a tab, since it can be confusing for the following reason: When you press Home in the text editor, you expect the cursor to jump to the beginning of the line as it is displayed, which (due to wrapping) may be different from the actual previous newline character.
• So you don't have to reach for the mouse to tab out of the editor you can press and release the Ctrl key, and the next key press will not be intercepted; thus Tab takes you out of the editor. Pressing and releasing Ctrl will grey out the text editor until the next keystroke to clarify this. If you think this is too awkward, I'm open to other suggestions, but there should be some way to tab out of the editor .

Note that this will never insert TAB characters, only spaces. It does however handle already-present TABs, and it handles them the same way the Markdown converter does.

A "format code" tool would imply

1. knowing how to format many different languages
2. picking a indentation style

The first is a hassle, the second an invitation to holy wars.

You shouldn't be typing significant bits of code directly into SO anyway, as you will generate spurious errors: cut and paste the code that you ran to show how it doesn't do what you hoped.

Format in your editor or IDE, already.

As has been said before, if you make Tab indent instead of moving between fields, you are breaking a fundamental UI feature. Please don't do this. Make Ctrl+K indent instead. Yes, it's less discoverable, but it beats breaking moving between fields. The problem with Ctrl+K is that it only supports a single level (which breaks in lists, in particular) — so fix that. Do not change the functionality of the Tab key.