- Does the longest road have to start and end with a settlement or city at each end?
- Can you make an infinite loop around a hex?
- Should there be a card that can destroy another player’s road, forcing them to take their road back?
This information is found in the Settlers of Catan Rules.
The requirement for longest road is only that you have a continuous road of at least 5 segments. Your own buildings (settlements or cities) will not affect this, however other players' buildings can be placed along your road to block it.
You count the road pieces that make up the road, not the length of the road from 'start' to 'finish'.
If you are the first player to build a continuous road of at least 5 individual road pieces, you take this special card...
The only requirement is that the road pieces included in the 'longest road' are connected end-to-end, ie. they don't fork.
Note: If your road network branches, you may only count the single longest branch for purposes of the longest road.
The Cities & Knights expansion does include a card that lets you remove one piece of road as long as at least one end of it doesn't touch any of that player's other pieces. [Answer provided by @ConMan]
Whether it should be included in the base game is definitely a subjective question. I often think it would be useful to have a way to remove even your own roads, just to reclaim the pieces. If such a card were added, it would seem more 'fair' if players could remove their own pieces too. (either for free, or at a price).