I have been lurking on the Mechanical Ivesting/Workshop message boards for some time. What amazes me is the size of some of the nontaxable portfolios.
My ? is: if one does not have access to a 401(K) plan, how does one build such a portfolio. My limited knowledge would say a combination of investing $2K/yr in IRA/Roth IRA for many years and getting good return on your investments. Is there some other vehicle outside of IRAs for building a nontaxable account that allows > $2K/yr?

You do not need to even go outside the confines of IRAs to do this. For the self-employed, Simple-IRAs and SEP-IRAs allow contributions far in excess of the meager 2k/yr limitation on Traditional and Roth IRAs. You can do a search on these terms, or take a look in the Taxes board, where these have been extensively discussed.
Of course, in this manic market, it has been possible to build up an amazing portfolio in a very short period of time, if you got lucky and had your entire portfolio in just a few high-flying stocks. Just 50k in Qualcomm over the past year or so would result in over half a million today.

Wavelength