Carbon nanotubes (CNTs), which are one-dimensional (1D) molecular conductors, have attracted considerable attention from viewpoints of the novel structures, electronic states, quantum phenomena, and also applications to new opt and electronic devices. However, mostly none reported on superconductivity (SC) and its correlation with 1D electron phenomena. In the present study, I report on SC with the world-highest transition temperature (T-c) of 12 K (1) in arrays of multi-walled CNTs (MWNTs) with entirely end-bonded electrode junction and (2) in highly uniform thin films of boron-doped single-walled CNTs (B-SWNTs). In the former one, I reveal correlation of SC with Tomonaga-Luttinger liquid (TLL) state, which is a collective phenomenon arising from repulsive Coulomb interaction between electrons confined in 1D ballistic charge transport regimes. In the latter one, I clarify correlation of SC with van Hove singularities (VHS) in electronic density of states (DOS) in the SWNT. Based on this thin film, I show fabrication of paper-like thin films consisting of pseudo two-dimensional network of weakly coupled B-SWNTs (the so-called Buckypaper) and show an enhancement of the onset T-c up to 19 K by applying only a small pressure. In Section 4, I discuss about possibility for realization of quantum spin entangler and quantum bit utilizing a hybrid system of CNTs/superconductor, which is associated with the Section 1. Because CNTs have strong spin coherence and possibly strong spin entanglement in spin singlet (Cooper pair), it must allow realization of quantum spin entangler and bit without decoherence problem in near future. The present observations will shed light to feasibility of CNTs as a 1D superconductor and also research of 1D electron correlation. They promise application to novel quantum devices.