In order to extract buildings, you should use very high resoltion satellite imagery having 1m or better spatial resolution.

Dear Kleomenis, WorldView and QuickBird are the best for this job. We used those products for building´s surface calculation for tax porpuses and it did perfectly. The latest products available have very good spatial and spectral resolution even for automatic extraction of info, but all depends of many conditions like presence of big trees, latitude, time of day in which the scene was taken, among others.http://www.digitalglobe.com/about/our-constellation and http://www.satimagingcorp.com/satellite-sensors/quickbird/

I agree with the aforementioned answers. But if you want to use free data, the only choise that you have is the Sentinel-2 (10m s.r.), or you can look in earth explorer http://earthexplorer.usgs.gov/, in commercial satellite (IKONOS-2, Orb-View 3, Historical SPOT) if there is any dataset in your study area.

Then, there is a lot of ways to detect an urban area (indexes, classifications), but their accuracy depending on if it is dense or sparse.

Two good options: High resolution satellite imagery and LiDAR data. You can combine both approaches in ArcGIS. 

Thank you all. I want to compute the morphological building index for my study area, so I am looking for free rs data of high accuracy...

You can download (free) High Resolution imagery using SAS.Planet http://www.sasgis.org/sasplaneta/ 

hi, let us know if u need building features extraction or it's enough urban area extraction. In the latter case may be sufficient  free data like landsat that provides also data for interesting diachronical survey.regards

Dear Francesco thank you,

I would need also building features extraction. Do you have any suggestion?

Regards.

In addition to high-resolution images, using an object-oriented approach may have better results.

Dr. Ozgun Ok maintains a satellite (IKONOS and QuickBird) building detection benchmark with ground truth data: http://biz.nevsehir.edu.tr/ozgunok/tr/407 

http://biz.nevsehir.edu.tr/ozgunok/tr/407

Article Automated Detection of Arbitrarily Shaped Buildings in Compl...

Article Building Detection From Monocular VHR Images by Integrated U...

Thank you all!

If it's available, airborne LiDAR is a clear favorite for building extraction, especially in areas with tall vegetation canopy.  LiDAR's ability to penetrate canopy is very helpful for distinguishing between foliage and rooftops, and it is usually flown during leaf-off conditions to maximize penetration.  Combining LiDAR with high resolution optical data may also help.