On iPhones, try 3001#12345# .

On Android it often depends on the specific model you have. Here are some for the Samsung S3:

#06# Show IMEI number

#0# LCD Test Menu

##4636##* user statistics and Phone Info

#0011# Displays status information for the GSM

#1234# View SW Version PDA, CSC, MODEM

#12580369# SW & HW Info

#197328640# Service Mode

#32489# (Ciphering Info)

#232337# Bluetooth Address

#232331# Bluetooth Test Mode

#232338# WLAN MAC Address

#232339# WLAN Test Mode

#0842# Vibra Motor Test Mode

#0782# Real Time Clock Test

#0673# Audio Test Mode

#0# General Test Mode

#2263# RF Band Selection

#872564# USB Logging Control

#4238378# GCF Configuration

#0283# Audio Loopback Control

#1575# GPS Control Menu

#3214789650# LBS Test Mode

#44336# Sofware Version Info

#7780# Factory Reset

27673855# Full Factory Reset

#0289# Melody Test Mode

#2663# TSP / TSK firmware update

#03# NAND Flash S/N

#0589# Light Sensor Test Mode

#0588# Proximity Sensor Test

#3282727336# Data Usage Status

#7594# Remap Shutdown to End Call TSK

#34971539# Camera Firmware

#528# WLAN Engineering Mode

#7412365# Camera Firmware Menu

#07# Test History

#3214789# GCF Mode Status

#272886# Auto Answer Selection

#8736364# OTA Update Menu

#301279# HSDPA/HSUPA Control Menu

#7353# Quick Test Menu

27674387264636# Sellout SMS / PCODE view

#7465625# View Phone Lock Status

7465625638# Configure Network Lock MCC/MNC

#7465625638# Insert Network Lock Keycode

##7780##* Factory data reset - Clears Google-account data, system and program settings and installed programs. system will not be deleted, and OEM programs, as well as My Documents (pictures, music, videos)