This compilation is done based on referred books and research online in all related forums regarding recommendation of good books for FEM/A.

Category 1-Practical Engineering Analysis Approach (Beginner and Intermediate level)
This category books are for beginners and intermediate users who are learning FE method/analysis software, Students who want to start using software, practicing stress analysts and all professional design engineers who do not want mathematics (still some of these books come with mathematics, which is essential to understand FEM/A). You can refer these books if you want practical guide on how to setup problems and how to avoid errors in analysis and its rectification. These books emphasize on practical aspects of analysis problems.

1.Building Better products with Finite Element Analysis by Adams & Askenazi
2.Finite element modelling for stress analysis by R D Cook
3.Practical Stress Analysis with Finite Elements by Brian J. MacDonald
4.Practical Finite Element Analysis by S Deshpande, N Gokhale, S Bedekar and A Thite.
5.Finite element analysis: From concepts to applications by David S. Burnett
6.A Practical Guide to Reliable Finite Element Modelling by Alan Morris
7.The Finite Element Method and Applications in Engineering Using Ansys by Erdogan Madenci and Ibrahim Guven
8.The Finite Element Method - A practical course by G.R Liu & S.S Quek.
9.A First Course in Finite Elements by J Fish and T Belytschko
10.Understanding finite element stress analysis by John Robinson
11.NAFEMS Publications-

1.Finite Element Analysis for Engineers- A Primer by T.K. Hellen and A.A. Becker

2.A Designerâ€™s Guide to Simulation with Finite Element Analysis by V Adams

12.Finite Element Analysis for Design Engineers by Paul M. Kurowski
13.Finite Element Analysis and Design of Metal Structures by Ehab Ellobody, Ran Feng, Ben Young
14.Nonlinear Problems in Machine Design by Eliahu Zahavi, David M. Barlam

Category 2- Advance Engineering analysis, Academic, Research and Programming Approach (Advanced level)
This category books are for advanced users of FEA/M, Programmers, researchers, scholars, student, professors, teachers, academicians and professional engineers or anyone who want to learn theory and in depth knowledge of behind the screen calculations. These books emphasize more on theoretical aspects of analysis problems.

1.Finite element procedures by K J Bathe
2.Concepts and Applications of Finite Element Analysis by R D Cook, D Malkus, M. Plesha and R Witt.
3.The finite element method by O.C. Zienkiewicz and R.L. Taylor

1.Volume 1 The Basis

2.Volume 2 Solid Mechanics

3.Volume 3 Fluid Dynamics

4.The finite element method in engineering by S S Rao
5.The finite element analysis of shells by D Chappelle and K J Bathe
6.Fundamentals of Finite Element Analysis by David V Hutton
7.Finite Elements for Nonlinear Continua and Structure by Ted Belytschko
8.The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by Thomas J.R. Hughes
9.Introduction to Finite Element Analysis Using MATLAB and Abaqus by Amar Khennane
10.Introduction to Finite Elements in Engineering, by T R Chandrupatla and A Belegundu
11.A First Course in the Finite Element Method by Daryl L Logan
12.Programming the Finite Element Method by Smith and Griffiths
13.Computational Inelasticity by Simo and Hughes
14.Non-linear FEA of solids and structures Volume 1 and Volume 2 by Crisfield.
15.MATLAB Codes for Finite Element Analysis by A.J.M. Ferreira

In addition to these books, you can refer the particular software theory manuals for both categories, which are very informative and simple to understand.

Note- This list may not be unbiased since I have not completely read each and every book but just come across recommended books online. However, it can get you started immediately for required information.