Yes, gt and gT are the way to do this.

Admittedly I wouldn't personally recommend those mappings, because both already correspond to commands I use quite frequently. By default Y is synonym for yy, to yank a whole line, and T<char> moves back to the nearest instance of <char> on the current line. The first one I think people could live without, but the latter is kind of important for good vi.

It just might be me, but I always prefer multiple keys to pressing a dead key . After some time, my short finger cannot take it. For eg, I always use yy instead of Y.

Same here, but mine is

    nnoremap <Tab> gt
    nnoremap <S-Tab> gT

Normal mode tab switches through tabs. One (and two) key goodness.

That's a good one actually, I might switch over to that.

Unfortunately Tab is equivalent to ctrl-i, which I already use (jump forward in history list), so I can't use this in the end.