I'm currently interviewing for a position in a non-profit
organization.  The topics of compensation and bebefits have not come
up yet,but I would like to be a bit more prepared when they do.  My
question is: do non-profit organizations usually offer the same type
of benefits as for-profit organizations, i.e. health insurance,
vacations, sick-time, 401K, etc.?

I don't know what might be typical with regard to your potential
employer, or what might be typical across all non-profits, but, yes,
non-profit organizations do ofter at least some benefits like
vacations, health insurance, etc. that are at least comparable with
for-profit companies. (There may be some cases where a non-profit's
benefits package might be superior to a comparable for-profit company,
in recognition that the compensation itself may not be comparable.)

As for retirement, please note that many non-profits' retirement plans
are technically called 403(b) plans rather than 401(k)s, but function
in largely the same manner...

Good luck with your negotiations!