Should I sell my software application or giving it for free?

So I just finished the development of my software application. This is a tool intended to help webmasters to promote their websites in order they may get more traffic. I must add this software is not a spam tool. I have been in the search engine optimization and marketing environment for a while so I know this kind of software is very demanded, but there is also a lot of competition. On the other hand, I have noticed there is a lot of people who may not want to pay a dime for my software because they claim there are a lot of free tools out there. I know this is not true because I initially developed the software for my personal use because the lack of tools.

Initially, my idea was to sell the software. But it is getting really hard to even promote it.
Another idea is giving it for free just as a start up in order to get popularity and later I could sell some sort of premium licenses. My main concern is how to monetize my application while is free.

In the general sense, it really depends on exactly what type of application, and what kind of competition there is in the space. If the majority of competing software is offered for free, you had better have a heck of an application to be able to charge up front for it.

Most free applications are monetized through one or more of advertisements, premium versions with additional functionality, or support contracts. With a free app, you will see a higher conversion rate on your marketing investment, but that conversion rate may not lead to direct revenue, especially in the short term.

This is a very open ended question with no single correct answer. Without knowing anything about your app or your competition, I'd suggest calling it a public beta, offering it for free, but reserving the right to charge for it at a later date. Track your conversions, measure your users' successes, and market accordingly. If there is demand for more features, consider putting them in a premium version; hopefully by then you will have positive feedback and success stories, both of which make selling it up front easier.

Better yet, if I read the question correctly and this is a web marketing tool, use it to market itself. : )

Another option would be to split-test different landing pages to see which converts most profitably. For example, you could test a freemium version against a free-for-X-days version, or test a stripped-down version vs. a premium version at different price points.

The key to getting actionable results is to make sure you're testing with equivalent samples (same number of visitors, same times & days of the week, etc.). Google Analytics has tools that can help you set up these split tests, as do most e-mail marketing vendors (AWeber, etc.).

I have noticed there is a lot of people who may not want to pay a dime for my software because they claim there are a lot of free tools out there