Redirection

   command > filename        Redirect command output to a file

   command >> filename       APPEND into a file

   command < filename        Type a text file and pass the text to command

   commandA  |  commandB     Pipe the output from commandA into commandB

   commandA &  commandB      Run commandA and then run commandB
   commandA && commandB      Run commandA, if it succeeds then run commandB
   commandA || commandB      Run commandA, if it fails then run commandB

   commandA && commandB || commandC
                             If commandA succeeds run commandB, if it fails commandC

Success and failure are based on the Exit Code of the command.
In most cases the Exit Code is the same as the ErrorLevel

Numeric handles:

STDIN  = 0  Keyboard input
STDOUT = 1  Text output
STDERR = 2  Error text output
UNDEFINED = 3-9

   command 2> filename       Redirect any error message into a file
   command 2>> filename      Append any error message into a file
  (command)2> filename       Redirect any CMD.exe error into a file
   command > file 2>&1       Redirect errors and output to one file
   command > fileA 2> fileB  Redirect output and errors to separate files

   command 2>&1 >filename    This will fail!

Redirect to NUL (hide errors)

   command 2> nul            Redirect error messages to NUL
   command >nul 2>&1         Redirect error and output to NUL
   command >filename 2> nul  Redirect output to file but suppress error
  (command)>filename 2> nul  Redirect output to file but suppress CMD.exe errors

Any long filenames must be surrounded in "double quotes".
A CMD error is an error raised by the command processor itself rather than the program/command.

Redirection with > or 2> will overwrite any existing file.

You can also redirect to a printer with > PRN or >LPT1

Multiple commands on one line

In a batch file the default behaviour is to read and expand variables one line at a time, if you use & to run multiple commands on a single line, then any variable changes will not be visible until execution moves to the next line. For example:

 SET /P _cost="Enter the price: " & ECHO %_cost%

This behaviour can be changed using SETLOCAL EnableDelayedExpansion

Creating a new file

Create empty files using the NUL device:

Type NUL >EmptyFile.txt
or
Copy NUL EmptyFile.txt

To prevent the > and < characters from causing redirection, escape with a caret: ^> or ^<

Redirect multiple lines by bracketing a set of commands:

(
  Echo sample text1
  Echo sample text2
) > c:\logfile.txt 

Exit Codes

If the filename or command is not found then redirection will set an Exit Code of 1

Unicode

The CMD Shell can redirect ASCII/ANSI (the default) or Unicode (UCS-2 le) but not UTF-8.
This can be selected by launching CMD /A or CMD /U

With the default settings a UCS-2 file can be converted by redirecting it (note it's the redirection not the TYPE/MORE command that makes the encoding change)
TYPE unicode.txt > asciifile.txt

European characters like ABCàéÿ will usually convert correctly, but others like £¥ƒ€ will become random extended ASCII characters: œ¾Ÿ?

Pipes and CMD.exe

When a command is piped with '| batch_command ' this will instantiate a new CMD.exe instance, in effect running:

C:\Windows\system32\cmd.exe /C /S /D "batch_command"

This has several side effects:
Any newline (CR/LF) characters in the batch_command will be turned into & operators. (see StackOverflow)
If the batch_command includes any caret escape characters ^ they will need to be doubled up so that the escape survives into the new CMD shell.

Starting a new CMD shell also has a small (likely unnoticable) effect on performance.

For example, this syntax works, but would fail if the second or subsequent (piped) lines were indented with a space:
@Echo Off
echo abc def |^
find "abc" |^
find "def"> outfile.txt

Multi-line single commands with lots of parameters, can be indented as in this example:

Echo abc def ^
  ghi jkl ^
  mno pqr

When redirecting the output of DIR to a file, you may notice that the output file (if in the same folder) will be listed with a size of 0 bytes. The command interpreter first creates the empty destination file, then runs the DIR command and finally saves the redirected text into the file.

The maximum number of consecutive pipes is 2042

Examples:

   DIR >MyFileListing.txt
   
   DIR /o:n >"Another list of Files.txt"

   DIR C:\ >List_of_C.txt 2>errorlog.txt

   DIR C:\ >List_of_C.txt & DIR D:\ >List_of_D.txt

   ECHO y| DEL *.txt

   ECHO Some text ^<html tag^> more text

   COPY nul empty.txt

   MEM /C >>MemLog.txt

   Date /T >>MemLog.txt

   SORT < MyTextFile.txt

   SET _output=%_missing% 2>nul
   
   FIND /i "Jones" < names.txt >logfile.txt

   (TYPE logfile.txt >> newfile.txt) 2>nul

“Stupidity, outrage, vanity, cruelty, iniquity, bad faith, falsehood,
we fail to see the whole array when it is facing in the same direction as we” ~ Jean Rostand (French Historian)

Related:

conIN$ and conOUT$ behave like stdin and stdout, or 0 and 1 streams but only with internal commands.
SORT - Sort input.
CMD Syntax
TYPE - Display the contents of one or more text files.
Successive redirections explained (1>&3 ) - Stack Overflow.
Equivalent bash command (Linux): Redirection - Spooling output to a file, piping input.