core COMPANIES FOR ECE:

PSUs:
BHEL: http://www.bhel.com/home.php
ECIL: http://www.ecil.co.in/
BEL: http://www.bel-india.com/
NTPC: http://www.ntpc.co.in/
DRDO: http://drdo.gov.in/drdo/English/index.jsp?pg=homebody.jsp
ISRO: http://www.isro.org/
BSNL:  http://www.bsnl.co.in/
ONGC:  http://www.ongcindia.com/
HAL:  http://www.hal-india.com/
IOCL: http://www.iocl.com/
BPCL: http://www.bharatpetroleum.com/
GAIL:  http://www.gailonline.com/final_site/index.html
SAIL:  http://www.sail.co.in/
BARC: http://www.barc.ernet.in/
AAI: http://www.aai.aero/public_notices/aaisite_test/main_new.jsp

Other core companies for ECE:

Bharti Airtel Ltd.,Aircel,Idea,Spice,Vodafone,Virgin India,Tata Indicom,Reliance Infocomm,Connect Ping
Shyam Telecom Rajasthan
New Companies like Unitech, Videocon, etc. entering the telecom sector.
AT&T,Verizon India
Now other good companies are:Texas Instruments - US Company
Nokia India - Finland
Siemens - German Company
Honeywell India - US
Wipro (dealing in Chip Design)
Cadence (chip design related)
Infosys
TCS

List of companies in wireless communication:

    http://www.indiacatalog.com/web_directory/electronics/810.html