can non-profit organizations without tax status legally accept donations?

Answer 1

i think so
when you look at all the little local fund raisers that are always around

Answer 2

Sure, as long as they don't claim to have 501(c)3 status. Anyone can accept donations. The donors can't take a tax deduction for them though.

Answer 3

YES,
Nonprofits therefore are typically funded by donations from the private or public sector, and often have tax exempt status. Donations may sometimes be tax deductible. http://en.wikipedia.org/wiki/Non-profit_organization 501(c)(3)
Section 501(c)(3) is just one of the tax law provisions granting exemption from the federal income tax to non-profit organizations. This exemption does not cover other federal taxes such as employment taxes.
501(c)(3) exemptions apply to corporations, and any community chest, fund, or foundation, organized and operated exclusively for religious, charitable, scientific, testing for public safety, literary, or educational purposes, or to foster national or international amateur sports competition, or for the prevention of cruelty to children or animals.

Another provision, 26 U.S.C. § 170, provides a deduction, for federal income tax purposes, for some donors who make charitable contributions to most types of 501(c)(3) organizations, among others. Regulations specify which such deductions must be verifiable in order to be allowed (e.g., receipts for donations over $250).

Testing for public safety is described under section 509(a)(4) of the code which makes the organization a public charity and not a private foundation, but contributions to 509(a)(4) organizations are not deductible by the donor for federal income, estate, or gift tax purposes.
The most common 501(c) organizations include:
• 501(c)(1) — Corporations organized under acts of Congress such as Federal Credit Unions
• 501(c)(2) — Title holding corporations for exempt organizations
• 501(c)(3) — Various charitable, non-profit, religious, and educational organizations (see below)
• 501(c)(4) — Various political education organizations (see below)
• 501(c)(5) — Labor Unions and Agriculture
• 501(c)(6) — Business league and chamber of commerce organizations (see below)
• 501(c)(7) — Recreational club organizations
• 501(c)(8) — Fraternal beneficiary societies
• 501(c)(9) — Voluntary employee beneficiary associations
• 501(c)(10) — Fraternal lodge societies
• 501(c)(14) — Credit Unions
• 501(c)(19) or (23) — U.S. Veterans' posts and auxiliaries http://en.wikipedia.org/wiki/501(c)