My two cents worth...
I realize the posts are focused on credit cards that are pretty unrestricted on using points for travel, but I wanted to provide input on the way we approach this. We use a Marriott Visa card with the purpose of using their Marriott Rewards "travel packages" that include rt air plus 7 nights at a Marriott property. We've used this approach on 4 trips: Australia, Argentina, and two trips to Spain.
Our last two trips to Spain each required 215,000 points. I was able to obtain open jaws and stopovers on these trips that made it convenient to add in another 7 days in other parts of Spain. By this time next year, we'll have enough points to do it again
(assuming they don't bump up the point requirements.)
This approach works for us because we find Marriott properties that match our travel requirements and the flexibility offered by Capital One, for example (while attractive, I'll admit) isn't needed. I definitely appreciate Capital One's not charging an international transaction fee when making purchases outside the US and use it all the time in that arena. The Marriott Reward points can also be exchanged for air miles (eg. 50,000 air miles requires and exchange of 125,000 Marriott Reward points) but we've not taken this approach.