We present X-ray polarimetry observations from the Imaging X-ray Polarimetry Explorer (IXPE) of three low spectral peak and one intermediate spectral peak blazars, namely 3C 273, 3C 279, 3C 454.3, and S5 0716+714. For none of these objects was IXPE able to detect X-ray polarization at the 3σ level. However, we placed upper limits on the polarization degree at ∼10%–30%. The undetected polarizations favor models where the X-ray band is dominated by unpolarized photons upscattered by relativistic electrons in the jets of blazars, although hadronic models are not completely eliminated. We discuss the X-ray polarization upper limits in the context of our contemporaneous multiwavelength polarization campaigns.