Should I provide experimental results for a paper presenting an algorithm? In a paper I proposed an algorithm for something (extracting data from a webpage), I described the steps and the result of the algorithm using a sample webpage. Do I need provide experimental results on various websites?

Here I think my purpose is not to compare something with another thing, the precision of the algorithm depends on its input provided by the user, I just want to say the application based on this algorithm is easier to use by providing how the application works, and extendable to similar websites by justification its approach.

I am confused!, if I always for any algorithm I should provide experimental results, then please let me know by Yes always, if there are exception then please let me know what are those?
If your intention is to publish a paper in good journals and conferences then you have to show that your algorithm works in more than one case, just one page is not enough, except if that is the specific intention, lets say, collect data from Google Finance pages about each company. 

First prove correctness, which could be done formally, running a good number of different cases or just obtaining results that are similar to other established algorithm.

Also you have to prove the value of the algorithm, which could be done demonstrating his complexity using the big O notation; or benchmarking against other algorithms that solve the same problem. Eventually you will discover that the algorithm is better in some metrics (false positives/negatives, response time, memory usage, power, network traffic, ...) and not so good in others. 

I suggest that you verify how other algorithms are presented in the same area, specially in the journals or conferences that are good fit for it, and try to use the same methods and data sets. That will make easier for readers to evaluate how good is the algorithm when compared with others that solve the same problem.