Concierge services are available to perform a variety of errands , but most seem targetted at NRIs and corporates. The services offered include

Bill Payment Services
• Mobile Phone Bill
• Credit Card Bill
• Telephone Bill
• Electricity Bill
• Insurance Payment
• Loan Payment
• Others 

 Travel Services
• Railway Pass renewal
• Forex
• Vacation Packages
• Inter city buses
• Air and Railway Tickets  
 Entertainment / Ticket Bookings (Subject to Availability)
• Movies & Plays
• Theatres
• Music Concerts
• Major Events
 
 Postal Services
• Registered Post
• Ordinary Post
• Speed Post
• Book Post
• Telegram
• Money Order
• Purchase of stamps & envelopes
• Air mail
 
  Courier (Domestic, National & International) 
 
  Banking Services
• Cheque Depositing
• D.D. making
• Passbook Update  
 Event Management Services
 
• Fashion Shows
• Annual Parties
• Sporting events
• Product Launches
and Promotions
• Community Service Programs
• Theme Parties
• Catering services

Some of the companies / websites offering concierge services are:

yourmaninindia.com
www.saharacarehouse.com
concierge4india.com
indiasmanfriday.com
alaconcierge.com
lesconcierges.co.in
superseva.com
taskseveryday.com
brickworkindia.com