There are a variety of ways that allow for booting Linux in single user mode. The most common techniques involve passing a suitable option on the kernel command line (i.e. "single") or crashing the filesystem by power cycling the machine; this in turn will result in fsck being invoked at the next system start, which will sometimes drop you into single user mode.
Some Linux distributions do not require a password when entering single user mode. While this makes system administration somewhat easier, it is a considerable security problem. Make sure, that your system does not suffer from it.
For other security problems with running insecure programs under Linux or using poorly configured distributions, refer to the Usenet newsgroups, security mailing lists and choose a distribution whose manufacturer frequently releases security fixes. It is a fallacy to assume that the unavailability of patches implies the security and correctness of a software application; as a rule of thumb, a manufacturer who releases more patches than a different one, probably cares more about the security of your system than the latter. This also applies to operating systems other than Linux!