What e-commerce shopping cart modules are available?

osCommerce - http://www.oscommerce.com/
- OS Commerce is an industrial strength, highly configurable open source shopping cart platform that comes completely free with all domains. osCommerce is a fantastic platform to launch your e-commerce ventures

CubeCart - http://www.cubecart.com/
- Cube Cart provides SSL support, support for multiple payment options, personalized customer control panels and much more. Simple integration for 2Checkout, Authorize.net, WorldPay, PayPal, NOCHEX, E-Gold and other secure payment companies is also included.

Zen Cart - http://www.zen-cart.com/
- Zen Cart truly is the art of e-commerce; a free, user-friendly, open source shopping cart system. The software is being developed by group of like-minded shop owners, programmers, designers, and consultants that think e-commerce could be and should be done differently.

Agora shopping cart - http://www.agoracart.com/
- Agora Shopping Cart is a powerful online shopping / e-commerce solution that offers a wide range of out-of-the-box features that allows online stores to be setup in simple fashion for the beginner, yet it offers high power ecommerce, flexibility, and modular features that an experienced programmer or web designer will appreciate after seeing AgoraCart's full potential.

Who do you suggest for Merchant Accounts to process online orders?

HostingCity proudly uses e-onlinedata.com for its payment processing solutions. Check out there web site at http://www.e-onlinedata.com/.

I do not want to setup a shopping cart and/or merchant account myself, can you suggest any alternatives?

Here is a list of 3rd party shopping cart alternatives (they provide the shopping cart, all you need is products to sell and a hosting account).