Here's an example you can run as a batch script (copy-paste into a .bat file), using the SQLCMD utility in Sql Server client tools:

BACKUP:

echo off
cls
echo -- BACKUP DATABASE --
set /p DATABASENAME=Enter database name:

:: filename format Name-Date (eg MyDatabase-2009.5.19.bak)
set DATESTAMP=%DATE:~-4%.%DATE:~7,2%.%DATE:~4,2%
set BACKUPFILENAME=%CD%\%DATABASENAME%-%DATESTAMP%.bak
set SERVERNAME=your server name here
echo.

sqlcmd -E -S %SERVERNAME% -d master -Q "BACKUP DATABASE [%DATABASENAME%] TO DISK = N'%BACKUPFILENAME%' WITH INIT , NOUNLOAD , NAME = N'%DATABASENAME% backup', NOSKIP , STATS = 10, NOFORMAT"
echo.
pause

RESTORE:

echo off
cls
echo -- RESTORE DATABASE --
set /p BACKUPFILENAME=Enter backup file name:%CD%\
set /p DATABASENAME=Enter database name:
set SERVERNAME=your server name here
sqlcmd -E -S %SERVERNAME% -d master -Q "ALTER DATABASE [%DATABASENAME%] SET SINGLE_USER WITH ROLLBACK IMMEDIATE"

:: WARNING - delete the database, suits me
:: sqlcmd -E -S %SERVERNAME% -d master -Q "IF EXISTS (SELECT * FROM sysdatabases WHERE name=N'%DATABASENAME%' ) DROP DATABASE [%DATABASENAME%]"
:: sqlcmd -E -S %SERVERNAME% -d master -Q "CREATE DATABASE [%DATABASENAME%]"

:: restore
sqlcmd -E -S %SERVERNAME% -d master -Q "RESTORE DATABASE [%DATABASENAME%] FROM DISK = N'%CD%\%BACKUPFILENAME%' WITH REPLACE"

:: remap user/login (http://msdn.microsoft.com/en-us/library/ms174378.aspx)
sqlcmd -E -S %SERVERNAME% -d %DATABASENAME% -Q "sp_change_users_login 'Update_One', 'login-name', 'user-name'"
sqlcmd -E -S %SERVERNAME% -d master -Q "ALTER DATABASE [%DATABASENAME%] SET MULTI_USER"
echo.
pause

Seba Illingworth 's code, In case you need time in your file name (it gives 2014-02-21_1035)

echo off
cls
echo -- BACKUP DATABASE --
set /p DATABASENAME=Enter database name:
For /f "tokens=2-4 delims=/ " %%a in ('date /t') do (set mydate=%%c-%%a-%%b)
For /f "tokens=1-2 delims=/:" %%a in ("%TIME%") do (set mytime=%%a%%b)

:: filename format Name-Date (eg MyDatabase-2009.5.19.bak)
set DATESTAMP=%mydate%_%mytime%
set BACKUPFILENAME=%CD%\%DATABASENAME%-%DATESTAMP%.bak
set SERVERNAME=.
echo.

sqlcmd -E -S %SERVERNAME% -d master -Q "BACKUP DATABASE [%DATABASENAME%] TO DISK = N'%BACKUPFILENAME%' WITH INIT , NOUNLOAD , NAME = N'%DATABASENAME% backup', NOSKIP , STATS = 10, NOFORMAT"
echo.
pause

You can use sqlcmd to run a backup, or any other T-SQL script. You can find the detailed instructions and examples on various useful sqlcmd switches in this article: Working with the SQL Server command line (sqlcmd)

if you need the batch file to schedule the backup, the SQL management tools have scheduled tasks built in...

Combine Remove Old Backup files with above script then this can perform backup by a scheduler, keep last 10 backup files

echo off
:: set folder to save backup files ex. BACKUPPATH=c:\backup
set BACKUPPATH=<<back up folder here>>

:: set Sql Server location ex. set SERVERNAME=localhost\SQLEXPRESS
set SERVERNAME=<<sql host here>>

:: set Database name to backup
set DATABASENAME=<<db name here>>

:: filename format Name-Date (eg MyDatabase-2009-5-19_1700.bak)
For /f "tokens=2-4 delims=/ " %%a in ('date /t') do (set mydate=%%c-%%a-%%b)
For /f "tokens=1-2 delims=/:" %%a in ("%TIME%") do (set mytime=%%a%%b)

set DATESTAMP=%mydate%_%mytime%
set BACKUPFILENAME=%BACKUPPATH%\%DATABASENAME%-%DATESTAMP%.bak
echo.

sqlcmd -E -S %SERVERNAME% -d master -Q "BACKUP DATABASE [%DATABASENAME%] TO DISK = N'%BACKUPFILENAME%' WITH INIT , NOUNLOAD , NAME = N'%DATABASENAME% backup', NOSKIP , STATS = 10, NOFORMAT"
echo.

:: In this case, we are choosing to keep the most recent 10 files
:: Also, the files we are looking for have a 'bak' extension
for /f "skip=10 delims=" %%F in ('dir %BACKUPPATH%\*.bak /s/b/o-d/a-d') do del "%%F"

I am using SQL Server 2005 Express, and I had to enable Named Pipes connection to be able to backup from the Windows Command. My final script is this:

@echo off
set DB_NAME=Your_DB_Name
set BK_FILE=D:\DB_Backups\%DB_NAME%.bak
set DB_HOSTNAME=Your_DB_Hostname
echo.
echo.
echo Backing up %DB_NAME% to %BK_FILE%...
echo.
echo.
sqlcmd -E -S np:\\%DB_HOSTNAME%\pipe\MSSQL$SQLEXPRESS\sql\query -d master -Q "BACKUP DATABASE [%DB_NAME%] TO DISK = N'%BK_FILE%' WITH INIT , NOUNLOAD , NAME = N'%DB_NAME% backup', NOSKIP , STATS = 10, NOFORMAT"
echo.
echo Done!
echo.

It's working just fine here!!

batch + sqlcmd

As a rule, a command line backup script is needed in order to run it automatically. In addition to the backup itself, the script must do two more things:

1. Delete obsolete backups - if they are not deleted, then over time the hard disk space will run out, and storing backups indefinitely is not necessary.
2. Leave at least somewhere a notification about the result of the backup. - the easiest way is to display the notification in the Windows Event Log. In this case, the error can be found in Server Manager > Dashboard.

Here is a script to backup one database, clean up (delete obsolete backups), and write a notification to the Windows Event Log:

set DB_NAME=MyDatabaseName
set BACKUP_DIR=C:\Backups
set DAYS_TO_KEEP=0
echo "Starting backup of %DB_NAME% database..."
sqlcmd -E -S . -Q "BACKUP DATABASE %DB_NAME% TO DISK='%BACKUP_DIR%\%DB_NAME%_%date:/=-%_%time::=-%.bak' WITH INIT, COMPRESSION"
if %ERRORLEVEL% neq 0 (
    echo "Backup failed with error code %ERRORLEVEL%."
    eventcreate /T ERROR /L APPLICATION /ID 100 /D "SQL Server backup failed with error code %ERRORLEVEL%."
    goto end
)
echo "Deleting old backup files older than %DAYS_TO_KEEP% days in directory %BACKUP_DIR% ..."
forfiles /P "%BACKUP_DIR%" /M "%DB_NAME%*.bak" /D -%DAYS_TO_KEEP% /C 2>nul "cmd /c if @ISDIR==FALSE del @PATH"
echo Old backup files deleted successfully.
:end
echo "Script complete."

powershell + Backup-SqlDatabase

Batch scripts are quite limited. It is much more efficient to use PowerShell scripts. Moreover, it has modules for interacting with SQL Server directly.

Installing the SqlServer module:

Install-Module -Name SqlServer

Now, for example, Get-ChildItem command can be used to query the list of databases. Use Backup-SqlDatabase command to backup the databases. Here is the command to backup all databases in general:

Get-ChildItem "SQLSERVER:\SQL\[server-name]\[instance-name]\Databases" | Backup-SqlDatabase -BackupContainer "[backup-path]"

Here is an example:

Get-ChildItem "SQLSERVER:\SQL\MSI\DEFAULT\Databases" | Backup-SqlDatabase -BackupContainer "c:\Backups2\"

In principle, a very complex script can be written in PowerShell, which will be limited only by your needs.

Here is a sample script to send a backup to shared folder.

Learn more about Backup-SqlDatabase

Third-party command line backup utilities

Instead of writing a script yourself, a third-party backup utility can be used. For example SqlBak-CLI. An example of sending a backup to FTP.

Create a JSON file with settings for where to get the backup and where to send it:

{
    "source":
    {
        "type":"mssql",
        "source_name":"source-name",
        "data_source":".",
        "trust_server_certificate":true,
        "is_integrated_security":false,
        "user_name":"sa",
        "user_password":"*******",
        "backup_items":{
            "item_types":[
                "mssql_custom"
            ]
        }
    },
    "storages":[
        {
            "type":"ftp",
            "server_name":"backup-storage.com",
            "user_name":"ftp-user",
            "user_password":"*************",
            "path":"backups"
        }
    ]
}

To start a backup, use the following command:

sqlbak-cli run-backup --job-settings=backup-settings.json

More about SqlBak-CLI