The slot
This is the pinout of the cartridge slot:

Pin     Side A                          SideB
--------------------------------------------------------------
 1      A10     ...................     GND
 2      A9                              GND
 3      A11                             A23
 4      A8                              A22
 5      A12     ...................     A21
 6      A7                              A20
 7      A13                             A19
 8      A6                              GND
 9      A14                             n.c.?
10      A5      ...................     GND
11      A15                             n.c.?
12      A4                              GND
        N/A                             N/A
        N/A                             N/A
15      A16     ...................     A1
16      A3                              A0
17      A17                             GND or 68000 HALT???
18      A2                              /RES
19      A18                             /WR (RAM U23 Pin 12)
20      /ROM (CPU CE (U1..U4) Pin 57)   ??? (RAM U24 Pin 12)
21      GND                             /DIR (68000 R/W)
22      D31                             /ROM2 (CPU OE(LowWORD))
23      D16                             /ROM1 (CPU OE(HighWORD))
24      D23                             GND
25      D24     ...................     INT0 (DSP Pin ?)
26      D30                             INT1 (DSP Pin ?)
27      D17                             +10V (DIRECT)
28      D22                             n.c.
29      D25                             GND
30      D29     ...................     n.c.
31      D18                             DSP Pin ?
32      D21                             GND
33      D26                             68000 /RESETIN
34      D28                             CARD INSERT A
35      D19     ...................     CARD INSERT B
36      D20                             VCC
37      D27                             VCC
38      VCC                             ?
39      D15                             n.c.
40      D0      ...................     EEPROM SERIAL DATA/STATUS
41      D7                              n.c.
42      D8                              /GPIO0 (EEPROM CLOCK)
43      D14                             /GPIO1 (EEPROM SELECT)
44      D1                              /GPIO2 (DSP Pin ?)
45      D6      ...................     /GPIO3 (*DSP Pin ?)
46      D9                              /GPIO4 (DSP Pin ?)
47      D13                             DSP Pin ?
48      D2                              DSP Pin ?
49      D5                              DSP Pin ?
50      D10     ...................     DSP Pin ?
51      D12                             GND
52      D3                              68000 CLOCK 13.295453MHz
53      D4                              GND
54      D11     ...................     GND

The 16bit-ROM
Here is the pinout of the 42-leg ROM IC: 

               ----u----
      A18    1=|       |=42   VCC?
      A17    2=|       |=41   A 8
      A 7    3=|       |=40   A 9
      A 6    4=|       |=39   A10
      A 5    5=|       |=38   A11
      A 4    6=|       |=37   A12
      A 3    7=|       |=36   A13
      A 2    8=|       |=35   A14
      A 1    9=|       |=34   A15
      A 0   10=|       |=33   A16
      !CE   11=|       |=32   !BYTE
      GND   12=|       |=31   GND
      !OE   13=|       |=30   D15
      D 0   14=|       |=29   D 7
      D 8   15=|       |=28   D14
      D 1   16=|       |=27   D 6
      D 9   17=|       |=26   D13
      D 2   18=|       |=25   D 5
      D10   19=|       |=24   D12
      D 3   20=|       |=23   D 4
      D11   21=|       |=22   VCC
               ---------

The 128K*8bit ROM
Here is the pinout of the 32-leg ROM IC: 

               ----u----
      Vpp    1=|       |=32   VCC
      A16    2=|       |=31   PGM
      A15    3=|       |=30   NC
      A12    4=|       |=29   A14
      A 7    5=|       |=28   A13
      A 6    6=|       |=27   A 8
      A 5    7=|       |=26   A 9
      A 4    8=|       |=25   A11
      A 3    9=|       |=24   /OE
      A 2   10=|       |=23   A10
      A 1   11=|       |=22   /CE
      A 0   12=|       |=21   D 7
      D 0   13=|       |=20   D 6
      D 1   14=|       |=19   D 5
      D 2   15=|       |=18   D 4
      GND   16=|       |=17   D 3
               ---------

The 512K*8bit ROM
Here is the pinout of the 32-leg ROM IC: 

               ----u----
      VPP    1=|       |=32   VCC
      A16    2=|       |=31   A18
      A15    3=|       |=30   A17
      A12    4=|       |=29   A14
      A 7    5=|       |=28   A13
      A 6    6=|       |=27   A 8
      A 5    7=|       |=26   A 9
      A 4    8=|       |=25   A11
      A 3    9=|       |=24   /OE
      A 2   10=|       |=23   A10
      A 1   11=|       |=22   /CE
      A 0   12=|       |=21   D 7
      D 0   13=|       |=20   D 6
      D 1   14=|       |=19   D 5
      D 2   15=|       |=18   D 4
      GND   16=|       |=17   D 3
               ---------


The EEPROM

The chip in the cartridge, that is used to save highscores or small 
amounts of save game data is a National Semiconductor NM93C14 
compatible chip.
This EEPROM has 128 bytes, which is organized as 64 16 bit words.
Each cell is addressed by a number from $0 to $3F.  The chip can be 
accessed with a maximum speed of 1 MHz and promises to have a 
lifespan of 15 years.
It is advertised to sustain at least 100000 read/write accesses. 
This means (according to National Semiconductor, who I asked about
this) datachanges on the whole chip. This isn't a whole lot really; 
running a tight loop you can exhaust this in approximately 3 seconds. 
Or to put this in another perspective, if you had a video game that 
would update the complete EEPROM after each game, you could play -safely-
ca. 1500 games.
It is therefore smart to minimize accesses to the EEPROM. I suggest 
that at the start of your code, you read the values from all of the 
cells that you are going to use  (not all of the EEPROM) completely 
and keep a local copy.
When ever you need to save changes, compare your data with the 
previous shadow copy and only update those cells that need it.

The 128K*8 Flash-PEROM
Here is the pinout of the ATMEL 29C010 12JC (PLCC32):
 
               A12 A16 Vcc  NC
                |   |   |   |
                |A15| NC|/WE|
                | | | | 3 3 3
                4 3 2 1 2 1 0
                - - - - - - -
      A 7    5=|      o      |=29   A14
      A 6    6=|             |=28   A13
      A 5    7=|             |=27   A 8
      A 4    8=|             |=26   A 9
      A 3    9=|             |=25   A11
      A 2   10=|             |=24   /OE
      A 1   11=|             |=23   A10
      A 0   12=|             |=22   /CE
      D 0   13=|             |=21   D 7
                - - - - - - -
                1 1 1 1 1 1 2
                4 5 6 7 8 9 0
                | D2| D3| D5|
                |   |   |   |
                D1 GND  D4  D6