Turing Machine restrictions that render halting decidable
A fairly natural and studied variation is the Tape-Reversal Bounded Turing machine (the number of tape-reversals are bounded); see for example:

Juris Hartmanis: Tape-Reversal Bounded Turing Machine Computations. J. Comput. Syst. Sci. 2(2): 117-135 (1968)

Edit: [this variation is more artificial] the halting problem is decidable for a Non-erasing Turing machine that has at most two left instructions on alphabet $\{0,1\}$; see Maurice Margenstern: Nonerasing Turing Machines: A Frontier Between a Decidable Halting Problem and Universality. Theor. Comput. Sci. 129(2): 419-424 (1994)