How Appealing noted an opinion by Judge Frank Easterbrook last week, to point out (among other things) that "Judge Easterbrook does not forgo using 'forego' to mean 'to do without.'" (The full phrase in the opinion was "the insurers contend that Freedom's willingness to forego the collection of any deficiency ....")
There is indeed a common assertion that "go without" should only be written "forgo," and "go before" should only be written "forego," as in "the foregoing." ("The E in “forego” tells you it has to do with going before. It occurs mainly in the expression “foregone conclusion,” a conclusion arrived at in advance. “Forgo” means to abstain from or do without. “After finishing his steak, he decided to forgo the blueberry cheesecake.”") Bryan Garner's Oxford Dictionary of American Usage and Style largely echoes this. (I'm not sure about Howard Bashman's views; he may well have just been referring to the assertion, and not endorsing it.)
And indeed, it sounds logical that "foregoing" should correspond to "going before" and not "going without." But it's also logical to denounce "its" as a possessive of "it" (the rule for most possessive is to add an apostrophe and an "s" rather than just an "s"), "aren't I?" as short for "am I not?," and "himself" (shouldn't it be "hisself," by analogy to "myself," and because we're talking about his self?). Logic takes you only so far when we're talking about English, and I imagine all or nearly all other languages.
So as these examples — and many more — illustrate, it is important to look to "the will of custom, in whose power is the decision and right and standard of language." And modern search technology makes it very easy to see what the custom is. A Westlaw search for "to #forgo" & date(> 1/1/2008) yields 916 hits; a Westlaw search for "to #forego" & date(> 1/1/2008) yields 1914. (The "#" is required to prevent Westlaw for searching for both, since it otherwise recognizes them as synonyms.) Quick eyeballing of reveals that these seem to mean "to go without," which makes sense: "To forego" in the sense of "to go before" would be a pretty odd locution. Googling reveals that this isn't just legal usage; "to forego" beats "to forgo," though by a smaller margin (1.74M reported hits vs. 1.56M). So both "forego" and "forgo" are in common usage to mean "go without"; custom approves of both.
Ah, some may say, that's just a sign of how the language is going to hell in these degenerate times. But the preference for "to forego" over "to forgo" seems to have been much stronger in past decades. Limiting the search to cases before 1940 yields 2626 cases for of "to forego" and only 9 for "to forgo." Either there's some serious glitch in Westlaw (unlikely; I get the same results with Lexis), or past usage is overwhelmingly in favor of writing "to do without" as "to forego" rather than "to forgo."
So it's hard for me to see any basis for condemning the use of "to forego" in the sense of "to do without." Logic, as I mentioned, doesn't tell us much. Modern usage, including in edited prose written by generally quite literate judges and law clerks, suggests that both "to forego" and "to forgo" are acceptable. Longstanding usage, at least longstanding legal usage, suggests that if anything "to forego" is more standard (though I wouldn't condemn "to forgo" on account of this; I'd say both are proper). There's no risk that "to forego" as "to do without" will be unclear to the reader; context pretty much always dispels any possible risk of confusion.
So all we have to criticize the "forego = do without" usage is basically some people's aesthetic judgment. If you share that aesthetic judgment, then by all means use "forgo." And even if you don't share the judgment, you might still want to avoid "forego = do without" in order to satisfy the purists, on the theory that today "to forgo" is the safe bet, though perhaps it wasn't in the past (at least in legal usage). But I see no real foundation for any claim that "forego = do without" is wrong, a "mistake," or even "poor usage."
UPDATE: "Esthetic" changed to "aesthetic," following commenter Mark N., Horace, and Google. Not that there's anything wrong with "esthetic," mind you ....