The boot messages come in two parts: those that come from the kernel (loading drivers, detecting partitions, etc) and those that come from the services starting up ([ OK ] Starting Apache...). The kernel messages are stored in /var/log/kern.log and can also be accessed from the kernel’s own log buffer with the dmesg program.
The userspace messages are not stored anywhere unless you install the bootlogd package. It will log the service startup messages in /var/log/boot Note if you have the “fancy” boot messages (the colored [ OK ] [FAIL] etc messages), it will log the terminal escape codes in the file. You can disable the fancy boot messages by creating an /etc/lsb-base-logging.sh shell script which defines FANCYTTY=0 in it.