There are probably many ways to classify microarray "types"; I don't know that any of them are very meaningful or useful.

You could start by visiting NCBI GEO Platforms browser, from where you can export data (in chunks of 5000 records). I loaded that data into R and ran table() over the "Technology" column, for this result.

> as.data.frame(table(platforms$Technology))
                                 Var1 Freq
1                                        1
2                            antibody   24
3          high-throughput sequencing 1908
4             in situ oligonucleotide 5524
5  mixed spotted oligonucleotide/cDNA   16
6                                MPSS   18
7                                  MS   17
8               oligonucleotide beads  223
9                               other  164
10                             RT-PCR  268
11                        SAGE NlaIII   67
12                          SAGE RsaI    1
13                         SAGE Sau3A    4
14                              SARST    2
15                   spotted DNA/cDNA 2859
16            spotted oligonucleotide 2831
17         spotted peptide or protein  105