Opera 12 Alpha web browser got released recently, and I think it is one of the fastest web browser for older computer with less then 1GB of RAM , and a 1GHZ CPU. Opera will run super fast on mid to high end computers with a 2.0-3.0 GHZ multi-core CPU, 4GB of RAM or more. I am currently using Opera 12 Alpha version on a computer with a 1.8 GHZ dual core CPU, and 1 GB of RAM running Windows 7, and Opera runs fast on my slightly slower computer.
I like that Opera is very easy to customize, I can hide the address bar, move the address bar to the bottom of the screen, and move the tab bar to the bottom of the screen to give the allusion of having more screen space since I rarely look at the very bottom of the screen. I can also hide the status bar, and the sidebar dock at the left of the screen very easily. The user interface is also very clean. I like that there is a zoom in and zoom out slider on the bottom right of the browser.
The mouse gestures when you hold down the right click button is also very good. All you do is hold down the right mouse button and move your mouse left to go back, right to go forward. Move your mouse up to stop, down for new tab.
The most useful shortcut key is CTRL+W for closed tab, CTRL+T for new tab, CTRL+TAB to switch tabs, and F2 to bring up a pop-up address bar, so you don’t have to move your mouse to the address bar, or click F8 to highlight the address bar.
Clicking F11 will make Opera go full screen and back to regular screen.
Opera also starts up pretty quickly when I click on the shortcut icon for the first time when opening Opera after I turned on Windows.
The Turbo Mode in Opera is useful for when my internet is slow, or I’m on a slower connection like dial-up, budget priced broadband with low bandwidth, or at a wi-fi hotspot with plenty of users. The download speeds for files like MP3, EXE, and other files I download on website links with Opera also seem a bit faster then other browsers like Internet Explorer 9.
Opera also is starting to have more add-ons like Lastpass, and different themes which you can install on Opera.
Opera also supports 3D applications with OpenGL , WebGL, and DirectX is coming soon. Opera can also use your video card to make Opera even faster.
Opera also supports Flash, Java, and other popular web plug-ins you find on YouTube, and other sites.
Opera 12 is also HTML5 compatible which means you can watch YouTube with YouTube’s new HTML5 player. The memory usage is also lower for Oper 12 which means you will have a 40% faster loading times on secure websites, and  use 30% memory when running JavaScript in your browser.
With Opera 12, you can now change the background image for your speed dial/ custom bookmarks new tab page very easily, and now designers can create new themes in Opera 12 more easily then the past.
The Address bar in Opera now offers better search suggestions, and better results for history and bookmarks or speed dial at once.
Opera also has a link/URL checker which checks links, and website addresses which you click on  to make sure the website you are visiting has any know malware, spyware, or virus programs. If you are about to visit a website with a known virus on it, Opera will warn you  before you visit it.
Lastly, Opera 12 still maintains an Acid Web browser test of 100/100 at acid3.acidtests.org which means Opera will display most popular websites correctly.
Opera 12 Alpha works on Windows, Linux, Mac, FreeBSD, and Solaris Operating Systems for PC.
You can download or learn more about Opera 12 Alpha at Opera.com/browser/next
If you want to download the non-Alpha version of Opera which is Opera 11.51 , you can download it at Opera.com