My all time favourite is CTF in the Far Cry series. I love Steal the sample so much that I even made an account to post about it.
Similar to Timesplitters with carrier only able to carry half a dual weapon. However, the flag carrier could throw the flag (a baton) like a football.
An excellent way to destabilize any sort of camping in the base, it really made teams fight it out for control of key points on the map.
Add to this that the flag carrier was able to sprint and drive vehicles (the quad is the best vehicle in any game) and you have a very difficult to defend flag.
The focus wasn't so much on offense and defense, but moreso on who was where and who had what spot in the middle of the map. If the flag carrier wasn't supported by teammates in the middle then he wouldn't make it to the base unless he pulled off something amazing or sneaky.
It could go from a slow, controlled game to a frantic mess so quickly.
That game rewarded skill so much but was accessible to any sort of play style. It's sad that no game has matched that to this day, except for maybe TF2.
I miss that game so much.