On my test system (a mail server), these are the applications I stopped.
All but the last three I manually installed. I stopped cron so scheduled programs
would not run and stopping sysklogd turns off system logging.

/etc/init.d/postfix stop
/etc/init.d/amavis stop
/etc/init.d/clamav-daemon stop
/etc/init.d/clamav-freshclam stop
/etc/init.d/courier-imap stop
/etc/init.d/courier-imap-ssl stop
/etc/init.d/courier-pop stop
/etc/init.d/courier-pop-ssl stop
/etc/init.d/courier-authdaemon stop
/etc/init.d/apache-ssl stop
/etc/init.d/mysql stop
/etc/init.d/bind9 stop
/etc/init.d/ntp stop
/etc/init.d/atd stop
/etc/init.d/cron stop
/etc/init.d/sysklogd stop

These (important system processes) were left running:

msa:~# ps aux
USER       PID %CPU %MEM    VSZ   RSS TTY      STAT START   TIME COMMAND
root         1  0.1  0.1   1948   652 ?        Ss   09:00   0:01 init [2]
root         2  0.0  0.0      0     0 ?        S    09:00   0:00 [migration/0]
root         3  0.0  0.0      0     0 ?        SN   09:00   0:00 [ksoftirqd/0]
root         4  0.0  0.0      0     0 ?        S<   09:00   0:00 [events/0]
root         5  0.0  0.0      0     0 ?        S<   09:00   0:00 [khelper]
root         6  0.0  0.0      0     0 ?        S<   09:00   0:00 [kthread]
root         9  0.0  0.0      0     0 ?        S<   09:00   0:00 [kblockd/0]
root        10  0.0  0.0      0     0 ?        S<   09:00   0:00 [kacpid]
root        85  0.0  0.0      0     0 ?        S<   09:00   0:00 [kseriod]
root       121  0.0  0.0      0     0 ?        S    09:00   0:00 [pdflush]
root       122  0.0  0.0      0     0 ?        S    09:00   0:00 [pdflush]
root       123  0.0  0.0      0     0 ?        S<   09:00   0:00 [kswapd0]
root       124  0.0  0.0      0     0 ?        S<   09:00   0:00 [aio/0]
root       629  0.0  0.0      0     0 ?        S<   09:00   0:00 [khubd]
root       955  0.0  0.0      0     0 ?        S<   09:00   0:00 [md0_raid1]
root       959  0.0  0.0      0     0 ?        S<   09:00   0:00 [md1_raid1]
root      1033  0.0  0.0      0     0 ?        S<   09:00   0:00 [kjournald]
root      1212  0.0  0.1   2180   596 ?        S<s  09:00   0:00 udevd --daemon
root      1561  0.0  0.0      0     0 ?        S<   09:00   0:00 [kpsmoused]
root      1777  0.0  0.0      0     0 ?        S<   09:00   0:00 [kmirrord]
root      1813  0.0  0.0      0     0 ?        S<   09:00   0:00 [kjournald]
root      2155  0.0  0.0   1580   380 ?        Ss   09:00   0:00 /sbin/klogd -x
root      2389  0.0  0.1   1576   560 ?        Ss   09:01   0:00 /usr/sbin/acpid -c /etc/acpi/events -s /var/run/acpid.socket
root      2632  0.0  0.2   4924  1080 ?        Ss   09:01   0:00 /usr/sbin/sshd
root      2693  0.0  0.1   2180   816 ?        Ss   09:01   0:00 /sbin/mdadm --monitor --pid-file /var/run/mdadm/monitor.pid --daemonise --scan --syslog
root      2813  0.0  0.0   1572   492 tty1     Ss+  09:01   0:00 /sbin/getty 38400 tty1
root      2814  0.0  0.0   1572   492 tty2     Ss+  09:01   0:00 /sbin/getty 38400 tty2
root      2815  0.0  0.0   1572   492 tty3     Ss+  09:01   0:00 /sbin/getty 38400 tty3
root      2816  0.0  0.0   1572   492 tty4     Ss+  09:01   0:00 /sbin/getty 38400 tty4
root      2817  0.0  0.0   1572   492 tty5     Ss+  09:01   0:00 /sbin/getty 38400 tty5
root      2829  0.0  0.0   1572   492 tty6     Ss+  09:01   0:00 /sbin/getty 38400 tty6
root      3841  0.0  0.4   7864  2360 ?        Ss   09:01   0:00 sshd: root@pts/0
root      3843  0.0  0.3   4276  1772 pts/0    Ss   09:01   0:00 -bash