I chose to pay my house off early and I'm sure glad I did. It will be paid off in about 5 years and that will open a lot of doors for me. I will have shaved 9 years off the loan and paid it off in 21 years, instead of 30.
Instead of signing up for a biweekly plan, I simply paid extra each month. This doesn't require any extra fees or changes to your billing schedule and it's very effective. It's also very flexible. When I was laid off for six months, I just went back to paying the minimum. When I run into some extra money, I can make an even bigger payment. It's as simple as that.
The only to remember about this strategy, is to start right away. The sooner you start paying extra, the bigger of an impact it has. At the beginning of the loan, just paying an extra couple hundred bucks is like making a double payment. If you wait until the end of the loan, it doesn't make a big difference on the interest you will pay.

I totally agree with paying off the house faster, for the same reasons Shenandoah said. That puts you in a much better position to handle long-term turbulence in your personal finances.

While it would be nice if everyone understood investing well enough to pull off Brave New Life's plan, most people don't. And so, for most people, a paid off house is actually one of the best "retirement funds" they can have. Not having a monthly housing payment once you're on a fixed income is HUGE.
My MIL pays 41.5% of her fixed monthly income on housing costs- and she lives in income restricted housing. (By comparison, we pay about 33% of our monthly income on housing costs- and that will go down as our incomes go up.)
I've actually been thinking about switching to bi-weekly payments for our mortgage, though not, funnily enough, because of the savings in interest rates. My biggest reason would be cash flow.
Right now, in the first 4 days of the month, we have bills due that add up to slightly more than 50% of our monthly income (based on 2 paychecks a month). Proportionally, that's a pretty huge hit. If something comes up and I'm not paying attention, that can cause problems. (I'm obsessive about tracking our cash flow, so it hasn't, but I've seen where it could have.)
If I were to switch the payments to every 2 weeks when I get paid, our cash flow would even out and the chances of a problem occurring decreases significantly.

I agree with you. Specially, in this real estate slump, the less money you have tied in to your house the better.
But I guess, if you can be sure that you will stay in the house for at least 10 years or more, you could think of refinancing for a 15 year mortgage.

The problem with a 15 year mortgage is that by paying off your loan faster you are tying up money for those 15 years rather than investing the money. With a 15-year window, it's likely you can beat 4% with a balanced portfolio of stocks and long term treasuries.
My alternative approach would be to get the lowest rate you can get on a 30 year loan, use the excess cash flow to save into a balanced portfolio, and once you have enough to pay off the mortgage entirely, decide whether you want to pay it off or continue to leverage the money.
Both options are good, it all comes down to your level of risk comfort.