With DMT and related substances this is all very possible. This means DMT, mushrooms, ayahuasca, etc. But also mescaline and cactus enable you to take a total plunge into other reality's.
Many people say that salvia does it as well, but with that i have no experience.
I wouldn't try it with MDMA or related compounds, since it is probably impossible and extremely high amounts are probably extremely unhealthy as well.
With cannabis you can get pretty far, but not so far that you get completely transported to another reality. If you take too much you just pass out or get sick.
LSD on itself can take you to the threshold of a breaktrough, but no further than that. In combination with harmala's though, it can induce true psychedelic breakthroughs as well.
There are many other substances that can bring you there with wich i have no experience, that are more exotic, harder to find or riskier:ibogaine, ketamine, PCP, or other novel tryptamines such as DPT.
I think those last substances would all require the presence of a sitter.
Of all these substances, DMT, ayahuasca, shrooms, mescalin and LSD+hamrala's, are the friendliest by far.
I would not try the others if i had no experience with powerfull breakthroughs.