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We describe the realization of Bose-Einstein condensates (BEC) of 87Rb atoms with relatively large number of atoms at high density, in laser-optical traps in our laboratory. Starting from a giant magneto-optical trap containing nearly 1010 atoms, we transfer about 5 x 107 atoms into the optical dipole trap formed by crossing two high-power focused CO2 laser beams. BEC containing about 105 atoms was produced by forced evaporative cooling of the atomic sample in the crossed optical trap down to about 140 nK, in just about a second. The BEC was also produced in a 1D optical lattice formed by the standing wave of a retroreflected focused CO2 laser beam, with about 80,000 atoms in the condensate. Effects of mean-field interaction characteristic of BEC were observed in the expansion dynamics of the condensate. We discuss both the techniques and the innovations that enabled the efficient execution of the multiple steps involved in producing the BEC, starting from a thermal sample of rubidium gas. [ABSTRACT FROM AUTHOR]