This paper presents the deepest 100 to 500 μm far-infrared observations obtained with the Herschel Space Observatory as part of the GOODS–Herschel key program. The authors examine the infrared (IR) spectral energy distributions (SEDs) of galaxies at 0 < z < 2.5, supplemented by a local reference sample from IRAS, ISO, Spitzer, and AKARI data. They determine the projected star formation densities of local galaxies from their radio and mid-IR continuum sizes. The study finds that the ratio of total IR luminosity to rest-frame 8 μm luminosity, IR8 (≈LIR/8), follows a Gaussian distribution centered on IR8=4 (σ=1.6), defining an IR main sequence for star-forming galaxies independent of redshift and luminosity. Outliers from this main sequence produce a tail skewed toward higher values of IR8, which consists of starbursts with compact projected star formation densities. IR8 can be used to separate galaxies with normal and extended modes of star formation from compact starbursts with high IR8, high projected IR surface brightness, and a high specific star formation rate. Locally, luminous and ultraluminous IR galaxies (U)LIRGs are systematically in the starburst mode, while most distant (U)LIRGs form stars in the "normal" main sequence mode. This confusion between two modes of star formation is the cause of the so-called "mid-IR excess" population of galaxies found at >1.5 by previous studies. The GOODS–Herschel observations demonstrate that incorrect extrapolations of total IR luminosity from 24 μm observations at z≤1.5 do not indicate a drastic evolution of IR SEDs or the ubiquity of warm AGN-heated dust dominating the mid-IR emission. Instead, the universality of IR8 among main sequence star-forming galaxies allows for the distinction between a majority of "main sequence" (MS) galaxies and a minority of compact "starbursts" (SB). The IR main sequence is shown to correlate closely with the IR surface brightness and the projected star formation density, and with the starburst intensity, quantified as "starburstness." The study also presents evidence that the mid-to-far IR emission of X-ray active galactic nuclei (AGN) is predominantly produced by star formation and that candidate dusty AGNs with a power-law emission in the mid-IR systematically occur in compact, dusty starbursts. After correcting for the effect of starbursts on IR8, new candidates for extremely obscured AGNs are identified.This paper presents the deepest 100 to 500 μm far-infrared observations obtained with the Herschel Space Observatory as part of the GOODS–Herschel key program. The authors examine the infrared (IR) spectral energy distributions (SEDs) of galaxies at 0 < z < 2.5, supplemented by a local reference sample from IRAS, ISO, Spitzer, and AKARI data. They determine the projected star formation densities of local galaxies from their radio and mid-IR continuum sizes. The study finds that the ratio of total IR luminosity to rest-frame 8 μm luminosity, IR8 (≈LIR/8), follows a Gaussian distribution centered on IR8=4 (σ=1.6), defining an IR main sequence for star-forming galaxies independent of redshift and luminosity. Outliers from this main sequence produce a tail skewed toward higher values of IR8, which consists of starbursts with compact projected star formation densities. IR8 can be used to separate galaxies with normal and extended modes of star formation from compact starbursts with high IR8, high projected IR surface brightness, and a high specific star formation rate. Locally, luminous and ultraluminous IR galaxies (U)LIRGs are systematically in the starburst mode, while most distant (U)LIRGs form stars in the "normal" main sequence mode. This confusion between two modes of star formation is the cause of the so-called "mid-IR excess" population of galaxies found at >1.5 by previous studies. The GOODS–Herschel observations demonstrate that incorrect extrapolations of total IR luminosity from 24 μm observations at z≤1.5 do not indicate a drastic evolution of IR SEDs or the ubiquity of warm AGN-heated dust dominating the mid-IR emission. Instead, the universality of IR8 among main sequence star-forming galaxies allows for the distinction between a majority of "main sequence" (MS) galaxies and a minority of compact "starbursts" (SB). The IR main sequence is shown to correlate closely with the IR surface brightness and the projected star formation density, and with the starburst intensity, quantified as "starburstness." The study also presents evidence that the mid-to-far IR emission of X-ray active galactic nuclei (AGN) is predominantly produced by star formation and that candidate dusty AGNs with a power-law emission in the mid-IR systematically occur in compact, dusty starbursts. After correcting for the effect of starbursts on IR8, new candidates for extremely obscured AGNs are identified.