Intensity noise of mode-locked fiber lasers is characterized systematically for all major mode-locking regimes over a wide range of parameters. We find that equally low-noise performance can be obtained in all regimes. Losses in the cavity influence noise strongly without a clear trace in the pulse characteristics. Given that high-energy fiber laser oscillators reported to date have utilized large output coupling ratios, they are likely to have had high noise. Instabilities that occur at high pulse energies are characterized. Noise level is virtually independent of pulse energy below a threshold for the onset of nonlinearly induced instabilities. Continuous-wave peak formation and multiple pulsing influence noise performance moderately. At high energies, a noise outburst is encountered, resulting in up to 2 orders of magnitude increase in noise. These results effectively constitute guidelines for minimization of the laser noise in mode-locked fiber lasers.