Brownian dynamics simulations have been carried out to model attractive polymers in solution. Bead-spring polymer chains with attractions between the end beads were modeled over a wide concentration range on either side of the overlap concentration, rho*, for the corresponding random coil polymers. The polymers were treated as beads linked by finitely extensible nonlinear elastic springs and the excluded volume repulsion between unlinked beads was represented by a pair potential with a Gaussian analytic form. For the sticky end-beads the potential has an attractive tail of Gaussian form. In addition to chains with purely repulsive bead-bead nonbonded interactions, three different systems with attactive end beads were modeled. There were those with (a) head-head (H-H) attractions, (b) with both H-H and tail-tail (T-T) attractions, and (c) with head-tail (H-T) attractions. The dimensions of the chains, the bead-bead radial distribution functions, as well as the dynamic properties such as stress tensor time-correlation functions, infinity frequency elastic modulus, and specific viscosity of the solution were calculated as functions of solution density and end-bead attraction class. We show that with the three classes of attractive end-bead functionality, the model polymers all depart from random coil statistics and show evidence of enhanced association, even in the dilute regime, especially for the H-T systems, which can form necklacelike structures at low dilution and micellelike states with increasing concentration. (Not all of the polymer statistics measures show major differences though.) However, only the rheology if the H-T system is markedly different from the random coil case. The rheology of the H-T system is quite different in qualitative and quantitative behavior to the other classes studied. There is a progressive retardation and increasingly near-exponential decay in the shear stress relaxation function. The viscosity of the H-T class of polymers is typically at least an order of magnitude higher than that of the others, even at concentrations far below the overlap concentration rho* for such polymers. The infinite frequency elastic modulus is also typically about five times larger for the H-T class across the density range when compared with the other three types modeled.