They have all shown up in a space of ten years (a trivial span of time compared to their history) and all mostly on Earth, or in interactions with characters with close connections to Earth (i.e. Star-Lord and Thor).
The short answer is: Thanos.
For whatever reason, Thanos has begun looking for the Infinity Stones. This has caused at least two that had previously been dormant to resurface.
- The Mind Stone was given to Loki by Thanos to help him conquer Earth.
- The Power Stone was found by Star Lord because someone paid him (well, the Ravagers) to find it. We aren't given confirmation, but I think we can presume Thanos was the ultimate buyer.
Two others were on Earth already, long before the current series of movies began:
- The Space Stone was hidden by the Asgardians on Earth a long time ago, and rediscovered by the Nazis in the 1940s. The arrival of Thor finally prompted SHIELD to begin studying it.
- The Time Stone has been in the possession of the Masters of the Mystic Arts for a long time. It was never "hidden" -- the people who had it even seem to know what it was. They just kept it secret.
The only one that seems particularly suspicious is the Reality Stone. Of all the appearances of the stones, the fact that Jane Foster just so happened to walk through a portal that led to the Aether at the exact moment she did, is very convenient. In-universe, of course, it was time for the Convergence to happen, but Jane being in exactly the right place, and the portal going to exactly the right place, is the least-explainable part of the whole Infinity Stone saga.
Thor, for his part, seems to realize that "someone" is behind the sudden appearance of the stones. He makes the same comment you did at the end of Age of Ultron:
The Mind Stone is the fourth of the Infinity Stones to show up in the last few years. That's not a coincidence. Someone has been playing an intricate game and has made pawns of us.
Of course that someone is Thanos, and he's doing exactly what Thor thinks, but it's not clear that all of these appearances are his doing. I can't see how he could have influenced the Convergence, for example, or Odin's choice to exile Thor. However, Thanos seems to know a lot about these stones; he may have known that the Convergence was his only chance at the Reality Stone, and detected SHIELD messing with the Space Stone; that may explain why he picked this particular time to start his quest.
We already know that the Mind stone influences people, their ambitions and priorities. Thanos already has this prior to The Avengers, when he gives it to Loki as a tool to conquer Earth and retrieve the Space stone (the Tesseract). We saw it directly influence Bruce Banner, Strucker, Tony Stark, Ultron, and the Twins during their development.
This is pure speculation and opinion, but my theory is that the Mind stone, which governs and links into all consciousness in the Universe, is the true mastermind. It gave Thanos the knowledge, and idea of, bringing all the stones together to use as a weapon. It gave him subconscious knowledge of where to start looking for the other stones. This ties into the Order/Chaos aspect of the Marvel universe. It's never been fully established in the MCU that these entities truly exist or are accessible, but we've seen hints of it:
- Thanos grinning at 'courting death' in the Avengers post-credits scene
- Mordo using the Staff of the Living Tribunal during Doctor Strange; Dormammu and the alternate realities
- Odin's explanation of the Aether's origins and first major use during Thor: The Dark World
- The Collector's explanation of the source of the Infinity Stones during Guardians of the Galaxy with the artifact of the cosmic entities
- The first half of season 4 of Agents of S.H.I.E.L.D. with Ghost Rider
I think the Mind stone (the Consciousness of the Universe) is playing Thanos like a fiddle, partially driving (or multiplying) his desire to court/please Death, to eventually bring balance to the universe (since that ends up being the theme of all these grandiose deus-ex machina macguffin movies) because it knows Thanos will fail.