An alternative valediction to "godspeed" wishing someone success in a venture

"Goodbye" is derived from God be with you, as are many valedictions.

"Take care" is sort of threadbare. "Farewell" seems antiquated. "Bon Voyage" is great if you're French. Be well, good fortune, until we meet again
I do like the Vulcan Valediction, live long and prosper.

Namaste is very respectful. It is spiritual, however; it can be interpreted (roughly) as a way of saying "Not-myself to you" (a benevolent expression of both respect and impersonality). It has some good karma to it.

May the road be downhill all the way to your door.

May your days be many and your troubles be few. May peace be within you may your heart be strong. May you find what you're seeking wherever you roam.”

May the road rise up to meet you, may the wind be ever at your back. May the sun shine warm upon your face and the rain fall softly on your fields, until we meet again

There are many expressions of felicitations, to wish happiness, congratulations, longevity, success, or encouragement, that can be found in common use and that don't invoke a religious sentiment. I found this link, which seems to illustrate quite a few, some of which I quote here:

May you see your children's children.

May you be poor in misfortunes and rich in blessings.

May you know nothing but happiness from this day forward.

May the road rise up to meet you.

May the wind always be at your back.

May the sun shine warm upon your face, and rains fall soft upon your fields.

A common French expression that sometimes finds its way into English is bon courage, which might translate into keep a stiff upper lip, or hang in there, or simply you can do it.

Of course there is my half-joking comment above, which is live long and prosper. This, according to Phrase Finder originated as a Jewish religious blessing, but became more popular in Star Trek as the Vulcan salutation (along with the Vulcan hand salute.)

The same reference at Phrase Finder also equates this with the similar Hebrew phrase Shalom aleichem and the Arabic phrase Salaam alaykum that roughly translate to peace be upon you. This phrase was mentioned by others here.

As you can see, despite the fact that some of these phrases originated within a religious context, the words themselves, in many cases, are neutral toward religion.

Update

And in the same vein with the Star Trek reference, there is also may The Force be with you, which is an areligious Star Wars phrase probably borrowed from "may the Lord be with you". (Unless you subscribe to the notion that there is a religious cult aspect to The Force within the Star Wars universe.)

"Good luck" seems the most straightforward, and it might be a good place to start searching online thesauri if it's not exactly what you're going for.

Try, "Bon voyage!", "Peace be with you," "Farewell," or "Fare thee well." No divine intervention there. Also, "Good luck!" as mentioned by Kevin.

If you were a Spartan, "May you live forever," was actually the opposite, as the greatest glory a Spartan could achieve was dying in battle [1].

[1]: Source - 300

How about 'break a leg'. It is traditionally for actors and actresses but I've heard it used commonly.