The cheapest and simplest way to receive donations is to use a service such as Amazon's Simple Pay Donations that collects the money on their site. They give you a "click to give" button to put on your website, which takes a donor to Amazon's website, where he uses Amazon's regular payment forms to make his donation. The visitor can use whatever credit card he usually uses to buy stuff on Amazon. American Express has a version for Amex card owners. For Amex, your charity needs to be listed in Guidestar's database as an eligible recipient.
Network for Good is a good choice if your are a U.S. 501c3 with a tax id number and you get enough donations to warrant paying their monthly fee.
Grassroots.org offers discounted fundraising tools.
Paypal. has no up front charges. They take a small and just a percentage of what you receive in payments through them. That percentage is discounted for nonprofits. Essentially, they create buttons for you, based on a form you fill out, then you paste the button code onto your website. Here is their Getting Started guide.
This is a real win/win. A shopper signs up at an affinity site such as iGive.com, frequently getting coupons or discounts as a signing bonus. When he buys something online, part of the purchase price goes to the organization he designates. For the organization, this is free money. The only effort on the organization's part is asking their supporters, both online and in the real world, to patronize the affinity site's merchants. Another such site is Goodsearch.com. If you can get your supporters to use their search engine and their shopping site, they'll chip in part of their profits to your organization.
CafePress allows you to set up a store selling your own logo'd merchandise at absolutely no cost. Not only will you make a bit of money on each item sold, the people wearing your items will be giving you free advertising. CafePress takes care of all manufacturing, order tracking and shipping. All you have to do is design the items and collect the money.
Reader's Digest lets you sell magazines online through their www.eFundraising.com site. You can ask your supporters to help you by purchasing or extending their subscriptions through you. No cost to sign up.
For more information on fundraising on the internet, try these sites:
The Nonprofit Matrix
Articles about online fundraising, guide to affinity shopping, portal sites, etc.
Techsoup Articles and online community for nonprofits.