CAT Exam is not mandatory for admission in MBA Course. But if you want to get a Admission in Indian Institute of Management or other top B Schools then you have to appear in Common Admission Test and score well. Maximum all B-Schools in India Consider CAT Score

National Level MBA Entrance Exams other than CAT:

MAT( Conducts in February,May,September and December Months)
CMAT(Conducts Two Times in a year)
SNAP
TANCET
MH-CET
RMAT
GCET
PMET
XAT
GET
State Level MBA Entrance Exams
ICET

MBA Entrance Exams Main Topics:
Quantitative Aptitude
Data Interpretation
General Awareness
Verbal Ability
Logical Reasoning

Top MBA colleges of India accepting CAT Score are --

Indian Institute of Management Ahmedabad
Indian Institute of Management Bangalore
Indian Institute of Management Calcutta
Indian Institute of Management Lucknow
Institute of Rural Management Anand
Xaviers Labour Relation Institue Jamshedpur
Management Development Institute Gurgaon
Indian Institute of Management Indore
S.P. Jain Institute of Management and Research Mumbai
Indian Institute of Foreign Trade Delhi
Narsee Monjee Institute of Management Studies Mumbai
International Management Institute New Delhi
Faculty of Management Studies Delhi
Institute of Management Technology Ghaziabad
Jamnalal Bajaj Institute of Management Studies Mumbai
Xavier Institute of Management Bhubaneshwar
T.A. Pai Management Institute Manipal
Xavier Institute of Management & Entrepreneurship Bangalore
Fore School of Management New Delhi
Loyola Institute of Business Administration Chennai
Vinod Gupta School of Management IIT Kharagpur
Symbiosis Centre for Management and HRD Pune
NITIE Mumbai
Nirma Institute of Management Ahmedabad
K.J. Somaiya Institute of Management Studies and Research Mumbai
Department of Management Studies, REC Trichy
Department of Business Administration Aligarh
L.B. Shastri Institute of Management New Delhi
Symbiosis Institute of Business Management Pune
IILM New Delhi
ICFAI Business School Hyderabad
Goa Institute of Management Goa
Department of Management Studies, University of Madras Chennai
Indian Institute of Social Welfare and Business Management Kolkata
Vignana Jyothi Institute of Management Secunderabad
Graduate School of Business and Administration Ghaziabad
Prestige Institute of Management and Research Indore
ITUC School of Management Hyderabad
Institute of Productivity and Management Ghaziabad
School of Management Pondicherry
Institute of Management Development & Research Pune
Jaipuria Institute of Management Lucknow
BPHE's Institute of Management Studies, Career Devt & Research Ahmednagar
M.S. Patel Institute of Management Studies Baroda
Department of Business Administration, Vellore Engineering College Vellore
BK School of Business of Management Ahmedabad
Institute of Management in Kerala Thiruvananthapuram
School of Communication & Management Studies Cochin
Punjab School of Management Studies, Punjab University Patiala
Department of Business Administration Guwahati
SDM Institute for Management Development Mysore
Pt. Jawaharlal Nehru Institute of Business Management Ujjain
Badruka College Hyderabad
G.H. Patel PG Institute of Business Management Vallabh Vidya Nagar
Institute of Management Studies, Devi Ahilya University Indore
University Business School Chandigarh
IIAM Vizag
National Institute of Management Calcutta
R.A. Podar Institute of Management Jaipur
School of Business Management, Sri Venkateswara University Tirupati
Sri Sringeri Sharada Institute of Management New Delhi
Christ College Institute of Management Bangalore
Vaikunth Mehta National Institute of Cooperative Management Pune
IPE Hyderabad