What is a good, secure, method to do backups, for programmers who do research & development at home and cannot afford to lose any work?

Conditions:

1. The backups must ALWAYS be within reasonably easy reach.

2. Internet connection cannot be guaranteed to be always available.

3. The solution must be either FREE or priced within reason, and subject to 2 above.

Status Report

This is for now only considering free options.

The following open-source projects are suggested in the answers (here & elsewhere):

• BackupPC is a high-performance, enterprise-grade system for backing up Linux, WinXX and MacOSX PCs and laptops to a server's disk.
• Storebackup is a backup utility that stores files on other disks.
• mybackware: These scripts were developed to create SQL dump files for basic disaster recovery of small MySQL installations.
• Bacula is [...] to manage backup, recovery, and verification of computer data across a network of computers of different kinds. In technical terms, it is a network based backup program.
• AutoDL 2 and Sec-Bk: AutoDL 2 is a scalable transport independant automated file transfer system. It is suitable for uploading files from a staging server to every server on a production server farm [...] Sec-Bk is a set of simple utilities to securely back up files to a remote location, even a public storage location.
• rsnapshot is a filesystem snapshot utility for making backups of local and remote systems.
• rbme: Using rsync for backups [...] you get perpetual incremental backups that appear as full backups (for each day) and thus allow easy restore or further copying to tape etc.
• Duplicity backs directories by producing encrypted tar-format volumes and uploading them to a remote or local file server. [...] uses librsync, [for] incremental archives

Other Possibilities:

Using a Distributed Version Control System (DVCS) such as Git(/Easy Git), Bazaar, Mercurial answers the need to have the backup available locally.

Use free online storage space as a remote backup, e.g.: compress your work/backup directory and mail it to your gmail account.

Strategies

See crazyscot's answer