There are 23 L-amino acids that form the basis for proteins in all the known life on this planet. (The L- refers to the organization of the subgroups around the chiral carbon, or alpha carbon. D-amino acids be structural mirror images of L-amino acids.) All amino acids have the same "backbone", or basic structure:
    COOH
    |
H2N-C-H
    |
    R

where "R" represents the defining subgroup.

There are three "types" of amino acids, as defined by the polarity of their subgroups.
R groups only shown, except Proline. In parentheses are three-letter and one-letter abbreviations
The nonpolar (uncharged, hydrophobic) amino acids are:


Alanine (Ala, A):  -CH3
                       CH3
                       |
Isoleucine (Ile, I):  -CH-CH2-CH3

                        CH3
                        |
Leucine (Leu, L):  -CH2-CH-CH3

Methionine (Met, M):  -CH2-CH2-S-CH3

                               C=C
                              /   \
Phenylalanine (Phe, F): -CH2-C     C
                              \\ //
                               C-C

Proline (Pro, P):       COOH
                        |
                     HN-C-H
                      / |
                   H2C   CH2
                     \  /
                      CH2

Tryptophan (Trp, W):  -CH2-C=CH
                           | \
                           |  NH
                           | /
                           C-C
                          // \\
                         C     C
                          \   /
                           C=C

                  CH3
                  |
Valine (Val, V): -CH-CH3

The polar but uncharged amino acids are:
                          NH2
                          |
Asparagine (Asn, N): -CH2-C=O

Cysteine (Cys, C): -CH2-SH

Glycine (Gly, G): -H  
Note: Glycine is not chiral, because there are two identical subgroups (hydrogen).

                              NH2
                              |
Glutamine (Gln, Q):  -CH2-CH2-C=O

Serine (Ser, S):  -CH2-OH

                      OH
                      |
Threonine (Thr, T):  -CH-CH3


                           C=C
                          /   \
Tyrosine (Tyr, Y):  -CH2-C     C-OH
                          \\ //
                           C-C
The charged amino acids are:

Aspartate (Asp, D):  -CH2-COO-

                                    NH2
                                    |
Arginine (Arg, R):  -CH2-CH2-CH2-NH-C=NH2+

Histidine (His, H): -CH2-C-NH
                        //  \
                       HC    CH
                        \  //
                         NH+

Glutamate (Glu, E):  -CH2-CH2-COO-

Lysine (Lys, K):  -CH2-CH2-CH2-CH2-NH3+

There are other amino acids, such as ornithine, histamine, and thyroxine, which are modified amino acids found only in certain proteins or that occur as precursors during biosynthesis.
Structures redrawn from Garrett and Grisham, Biochemistry, 2nd edition