What are some reasons to sell a product below cost?

Lets say my company and another competitor are the only two contenders in a niche for a physical product. And the products are mostly similar (and can't really be altered much to have a big differentiation).

What are some ways we could sell it below cost to undercut out competitor and somehow many it profitable / break even in the long haul? Any examples of companies that have done or currently doing this?

One that comes to mind is Amazon Kindle.

Plenty of companies sell loss leaders and make it up in customer lifetime value. If you can upsell your customers, if a large enough portion of your customers will pay for higher scale, or if your product is a gateway to other purchases that you get a portion of (e.g. Kindle Fire -> app purchases), then you can turn a profit even if you're undercharging initially.

Unless you have enough cash reserves to run at a loss until you overtake the competition (as Daniel Que said) or start to see returns from customers making it all the way through a lifetime purchase cycle, the only other way is to make it cheaper for you to produce the product than for someone else to. Partner with a manufacturer or supplier, find a company willing to share the cost for marketing or cross-promotion, or find something you can leave out that isn't needed by a large enough portion of the market.

Companies like Amazon or Walmart are able to sell a product for less than the market average simply because they are so big and are making money elsewhere.

If you're a startup attempting to do this, you'd need to have some way to survive past those early times until the other company goes out of business or become severely crippled. Maybe this is due to large amounts of funding, or because you're making money elsewhere as a result of selling such a cheap product (maybe advertising).

Either way it sounds extremely risky.