Ok, so this issue has been happening to some extent since launch. It has only been since patch 2.2-2.3+ that it has become noticeably worse. To the point where it started as a minor annoyance, to now, severely hindering my gameplay experience (crashes every 30-60min). I almost expect when I teleport that there is a high likelihood that my client will crash. I am not exaggerating.

Replication:

Teleport to many different zones. Visiting higher population areas/zones will cause the crashes to occur sooner/faster.

It seems to be linked with memory usage. At approximately 1.4-1.45GB of RAM used by the ffxiv.exe the game will start freezing/locking up and eventually crashes.

Setup:
CPU: Intel i7-4770K @ 3.5GHz
Video Card: Sapphire R9 290
RAM: Gskill 16GB DDR3

Tests:
- Reinstalled FFXIV client from scratch - Same issue
- Updated AMD graphics drivers from 13.9 to 14.4 - Same issue
- Tested second spare R9 290 card - Same issue
Speculation:

The reason that I believe it is memory leak as others have discussed, is that as you teleport from zone to zone, the memory slowly increases until eventually it hits the 1.45GB mark and the game crashes.

I have friends running NVIDIA graphics cards and do not appear to have this issue. It might be limited to AMD graphics cards.

This evening, doing 9 treasure maps and 20 hunting log entries worth of teleporting caused 8 crashes. If I visited either Revenant's Toll or Limsa Lominsa during one of the sessions, the client would crash after visiting 3 zones.