Usually its safe to assume that sp2 hybridized atoms will be planar, but the bonds within the plane can be distorted from their ideal 120o angle.
If you're looking at a conjugated system, its usually safe to assume that will be planar too. The exceptions to this are things which can't be due to steric clash (e.g 2,4-dimethylpenta-1,3-diene), or antiaromaticity (cyclooctatetraene). In the case of aromatics, bond angles can be significantly distorted to achieve aromaticity, but once you get over about 8 ring members (cyclooctatetraenide dianion), you've got to start playing games with cis/trans geometry to get annulenes to hold together.