Open a new browser tab (winner: keybd)
Close a browser tab (winner: keybd)
Navigate forward/back in the history (winner: keybd)
Those are all arguably faster with gestures.
Ctrl+w versus mouse click while moving down, then right. Not sure who can possibly do that faster and with more accuracy than the most novice computer user.
Go to a history/bookmarked URL (winner: keybd)
With most browsers, I'd say this is true. With Opera's Speed Dial, it becomes a matter of whether you've memorized the name of the site (or bookmark). Just open a new tab, and you see a (fairly large) picture of each of your bookmarked sites. Click on the one you want to visit (or Ctrl+Number). This method makes both the keyboard and the mouse faster (and near-equivalent, IMO) by removing the dependence on the user's memory for speed.
This only advantageous for users who do not remember the names or URLs of the sites they want to visit, but recognize them by thumbnails. The mouse beating the keyboard suggests a certain increased level of stupidity on the part of the user.
Run an application (winner: keybd)
Only if you've memorized the name of the command. What you're really saying here is that searching for a program is slower than already having it memorized. I guarantee you that clicking on a desktop shortcut (and you have your dekstop set for single-click mode, right?) is faster than executing the key combo, then typing a word, then hitting enter.
Well, in Vista I can hit the window button, then start typing the name of the appliation (ie, word instead of winword.exe). Ditto for OS X using Spotlight (command+space). I would like to see anyone navigate through the start menu or finder to start Word faster (or even the Quick launch/Dock).
Cut/copy/paste/save/print/quit/etc (winner: keybd)
Cut,copy,paste is a process, not just a key combo. I've found that the process usually works best when you use both the keyboard and the mouse. The mouse is better for selecting large blocks of text and getting the cursor to the general area where you want it. The keyboard is better for precision movements.
Scrolling via arrow, pgup/dn, home/end vs. wheel (winner: keybd)
Let's have a race. We each have an identical several-hundred-page document. You use the page keys, I'll click on the scroll bar. First to the middle wins. Also, your mention of the scroll wheel belies your inexpertise with the mouse. The correct tool is the "middle-click drag" auto-scroll feature.
Of course I will win. With a 500-page documet, Ctrl+G, 250, enter. [Btw, I will ignore your pot shot at my inexpertise with the middle-click-drag only known to super 31337 users such as yourself.]
Switching between applications/windows (winner: keybd)
The advantage of the keyboard over the mouse is its parallel nature. Alt-tab is an inherently serial process, so it eliminates the advantage completely. (If you happen to know that the window you want is the previously-active window, then sure, alt-tab is inherently faster. But that's an incredibly special-case scenario.)
Switching to the previous application is incredibly special case? I generally have about 6 or 7 applications open at a time. I can easily cycle to the one I want to use far faster than anyone can locate what they want to use on a taskbar, most their mouse down and click it.
Click a link (Tie. I generally hit / and start typing the link text, hit escape, then enter to visit the link. Sometimes moving the mouse over the link is faster.)
That method is incredibly limited. You can't click on buttons or images. You lose context as you type since the screen's jumping around thanks to search-as-you-type. It fails miserably is the link text is repeated multiple times (eg "reply to this" on slashdot). IHBT. IHL. HAND.
Sure, it is limited, but it suffices most of the time. I am not averse to using a mouse when it is faster, it just rarely is. I often search twice to jump to the unique text before the repeated text.
While mouse gestures are certainly nice, they are, in my experience, far more prone to inaccuracy compared to a key presses. Mistakenly closing a browser tab happens far more often with gestures than the keyboard.
That is not at all my experience. Perhaps what you mean to say is that you are prone to imprecision with the mouse (especially if the next item is true for you). From this and other assertions of yours, the only conclusion I can make is that you're not very good with the mouse.
No need to get your panties in a bunch, but I can play too... From your assertions I can only conclude you are a slow, inaccurate typist with a poor memory. For those of us with good memories who can type quickly and accurately, the keyboard is always faster. Especially for those of us who were using computers since before Windows was viable and when the Mac was the least cool computer you could buy. Not that I am by any stretch a veteran, but I did learn to use computers at a time when the mouse was not very common.
Now, for the average Apple user who buys a MacBook to fit in with the crowd at his neighborhood Starbuck's, I have no doubt they are more capable using a mouse then a keyboard. Apple shouldn't have needed $50 million to figure that out.
[Just for the record, I would bet I am faster with a mouse than you. My slowness with a mouse is only relative to my speed with a keyboard. It doesn't actually mean you are faster.]