While the dream of immortality might be as old as mankind, the jellyfish Turritopsis nutricula (image) seems to be living it:

The hydrozoan Turritopsis nutricula has evolved a remarkable variation on this theme, and in so doing appears to have achieved immortality. The solitary medusa of this species can revert to its polyp stage after becoming sexually mature (Bavestrello et al., 1992; Piraino et al., 1996). In the laboratory, 100% of these medusae regularly undergo this change. Thus, it is possible that organismic death does not occur in this species!