Yes, conjugated dienes can react with other conjugated dienes in Diels-Alder reactions. A well known example of this is the dimerization of cyclopentadiene. All the standard caveats, restrictions, and other considerations still apply, namely:
- The diene must not be rotationally locked in such a way that it cannot adopt an s-cis/synperiplanar conformation. As a logical corollary, cyclic dienes that are already locked into the correct s-cis conformation often have lower activation barriers.
- The kinetics of the reaction are accelerated by electron-withdrawing substituents on the dienophile and electron-donating substituents on the diene.
- The stereochemistry of the major product is highly substrate-dependent. A preference for the endo isomer exists in cases where the dienophile has unsaturated substituents. In those cases, the transition state is stabilized by an overlap of the $\pi$-electron system between said unsaturated substituents and the $\pi$ orbitals of the newly forming double-bond at the back of the diene. (Just as a side note, Carey & Sundberg refer to this as the "Alder rule" in Advanced Organic Chemistry, but I've never seen that term used anywhere else.)
In principle, there's no reason why two conjugated $\pi$-bonds of a polyene cannot react similarly, provided they satisfy the orbital symmetry and conformational requirements and the reaction kinetics are favorable. Even aromatic molecules can undergo Diels-Alder reactions under the right set of conditions (see, for example, the Diels-Alder reaction between benzene and furan via a benzyne intermediate). There are also numerous instances of well-documented Diels-Alder reactions involving heteroatomic dienophiles, alkynes as dienophiles, polymerization reactions, etc.
If you can get your hands on the aforementioned Carey & Sundberg book, they discuss the Diels-Alder reaction at length (including relatively rigorous explanations of the stereospecifity and reaction kinetics via molecular orbital theory). If you're looking for a comprehensive reference, I doubt there's anything superior to the venerable March's Advanced Organic Chemistry. There's a chapter on Diels-Alder reactions (along with virtually every other organic chemistry reaction known to science), as well as a massive list of accumulated primary literature references if further detail is required.