Yes, you can connect an android phone to a TV or a computer monitor. At least if you have a new enough TV or monitor, and not a ten year old TV like I do. :-)
My android phone came with a HDMI cable to use when connecting phone to TV. I have connected it many times to my computer however, using a mini USB cable. But I would be able to use the HDMI as well, depending on what I want to do.
I am for sure no expert, but I have a Sony Ericsson experia arc S and I have used it for over a year. I hope that this answer is good enough to offer some help.
For newer phone, you may wish to use the following:
Micro USB to HDMI® MHL Adapter
Reference link: http://www.monoprice.com/products/product.asp?c_id=108&cp_id=10833&cs_id=1083314&p_id=8675&seq=1&format=2
Video link: http://www.youtube.com/watch?feature=player_embedded&v=P5tJl_a_wcc
In the reference link, it include information such as Compatible Mobile Devices (which you can retrieve from this link - http://www.mhlconsortium.org/WorkArea/DownloadAsset.aspx?id=5055)