Most experts, including Moore himself, expect Moore's Law to hold for at least another two decades.
A little math here: two decades is about 13 18-month periods. So doubling 13 times is 2^13, or a factor of 8192. Sqrt(8192) is ~90. So if ICs don't start to go 3D with their transistor layouts, then we need to fit ~90 times as many features in each dimension.
If the best current processes use 65 nm features, then improving that by a factor of 90 implies 0.7 nm, or 7 angstroms (Å). Atoms vary in diameter from 0.5 Å to 3.8 Å, with silicon being about 1.1 Å. So depending on the elements used in the IC, we would need to have features fewer than 7 atoms wide.
You can't make a transistor out of 7 atoms in a line, or 49 atoms in a square. The physical doping rates for IC transistors require about 1 atom per 1000
or fewer to be a doping atom - so you can theoretically build a transistor with 10000 atoms (~100 x 100 angstroms) of which 5-10 are dopants, but you can't build a transistor with 500 atoms of which 5-10 are dopants. In short, unless different materials are used (e.g. GaAs), we're rapidly approaching the size limit for ICs.
Moore's law is up against the wall. Without new technologies such as quantum or photon-based computing, or 3D chip fabrication, we won't see continued doubling in transistor count every 18 months. And we certainly won't see the growth rate continue for the next 2 decades.