In order to gain an appreciation for the general structure of warped gas layers in galaxies, we have constructed kinematical, tilted-ring models of 21 galaxies for which detailed H I observations already exist in the literature. In this paper we present results for the 15 normal spiral galaxies of this sample that are not viewed edge-on. A comparison between our models and tilted-ring models of the same galaxies previously constructed by other authors shows that there is generally good agreement. We make an attempt to unify the notation of diff&rent authors who have published radio observations and/or kinematical models of individual galaxies in this sample. We also suggest how, in future work of this nature, model parameters should be presented and referenced in order to maintain a reasonable degree of consistency in the literature.When viewed in the perspective of dynamical models, a twisted warped gas layer can be understood as arising from orbiting gas which is in the process of settling to a preferred orientation in the nonspherical, gravitational potential well of the galaxy. Hence, detailed kinematical modeling of a specific galaxy disk can provide not only information regarding the orientation and structure of its warp but also information about the shape (whether oblate or prolate) of the dark halo in which the disk is embedded. By examining a large number of galaxies in a consistent manner, we have deduced some general characteristics of warped disks that have heretofore gone unnoticed. We have also identified uniqueness problems that can arise in this type of modeling procedure which can considerably cloud one's ability to completely decipher an individual disk's structure. For 14 out of 15 spiral galaxies modeled here, we have been able to determine the local kinematical structure of the warp. Gas layers do not appear to warp more than ∼40° out of the plane defined by the central disk of the galaxy, but they can twist through angles as large as ∼170°. The overall position of the warp and the gross geometric shape of the halo have been determined unambiguously only in cases where the twisting of the warp is relatively strong. (Examples of galaxies whose disks sit in an oblate halo are M33, M83, NGC 2805, NGC 2841, and NGC 3718; prolate halos appear to surround NGC 5033 and NGC 5055; and ambiguous cases, at present permitting equally good oblate and prolate halo models, are M31, NGC 300, NGC 3079, NGC 3198, NGC 6946, NGC 7331, and IC 342). There appears to be a high degree of correlation between the twisting angles of kinematical models and precession angles derived from dynamical arguments. This correlation gives us considerable confidence that the kinematically identified twists in warped H I layers are real and that the general dynamical picture that has been put forward to explain their existence is correct. Adopting a scale-free, logarithmic halo potential having a quadrupole distortion η, we conclude specifically that in each of these twisted warped disk systems the product ητ8 is approximately equal to 1, where τ8 is the age of the warped layer in 108 yr.