In go, you start off blind. You have no sense of sight, touch, taste, or smell. All that there is are the stones and the board. One of the things that makes Go a truly unique game is that pretty close to the majority of a go player's career will be spent just learning how to see the board. From those that I've played against and talked to, I get the impression that until a player is about 6 kyu, their ability to see the board is simply limited.
It seems to me that 6 kyu is the final threshold of a sunday player. Up until this point, players learn basic shape, some measure of sabaki and joseki, and they start to learn whole board fighting. After 6 kyu, play strategy changes in the same way it does from 15 kyu to 10 kyu. If you're playing using the same tight shapes, and playing each game grabbing territory and then trying to wipe out the opponent's holdings with attacks that often go in too deep, then 6 kyu is as far as you can come. Because that's as far as you can get with a basic understanding of strategy, and it's as far as you'll get clinging to inflexible ideas of territory. To step beyond 6 kyu, the stakes of the game rise significantly.
For the 6 kyu player, or perhaps even the strategically advanced 7 and 8 kyu players, I would personally suggest abandoning themselves a little more to their games. Playing a strong game focused on gaining territory through whole board attacks, rather than simplistic territory grabbing may not yeild steady results at first, but will absolutely lead to a much more flexible understanding of the game, and eventually more wins. It's always more comfortable to grab territory and then bet the game on an unreasonable invasion into your opponent's territory late in the game, saying something like "if I don't jump in, then there's no way I can win." After all, because the situation gives your opponent so many chances to mess up, this can be a comfortable, if monotonous, way to play. However, from what I've seen, players find that this play style doesn't typically work out too well against stronger players.
No matter what your play style, if you'd like to try something new, then I may have a few suggestions. In a game where players are simply grabbing territory and depending on the strength of their well tested structures, there's typically some exciting fight at one time or another, but the options available on the game board are usually few, and a little boring, to boot. Territory grabbing is too simple. When playing dan level players, a comment that I've quite often heard, and have made myself, is that all of their plays seem to have so much weight!
Concept number one: "especially in the opening, if you grab territory without also threatening something (like punishing an opponent's group, etc.), then your move wasn't good enough, or fast enough." Personally, i think that this is a really strong way of playing. You make your territories by threatening to kill structures. With a method like this, if your opponent moves fast to squander your profit, you kill their group, or punish it in a way that provides enough thickness to make up for the difference. Naturally, some of you may think to the common concept that in the opening, once the corners are played, the next option is an approach or a corner enclosure. Certainly, a corner enclosure doesn't match this concept on face value, but the strength built up by a corner enclosure promises a strong attack on groups that enter the side because the corner group itself has become strong, and therefore exudes influence. Even if you're a large moyo style player, this concept is absolutely applicable. Speed, strength and influence come first; territory comes as a result of these two. This is the concept of strong and flexible moves, and it's what makes a player's moves so loaded with consideration.
Concept number two: "use the threat of the kill, but don't depend on it." I think this one is pretty self explanatory. It's never good to be stretched too thin, and it's dangerous to be put in a position like this. Even more, the influence and strength you can build by threatening to kill a group, can often be worth more than killing the group in terms of general play. Don't get too caught up. always remember to be flexible in your aims. If you push it too far, all will be for not.
Concept number three: "always consider what is par for the situation." This especially applies for odd moves and attack and defense in general, and it's a trick I learned from studying joseki. In many joseki problems, an answer will be considered incorrect because compared to another outcome, one stone may be placed better, or one more point might be captured in sente. The answer in itself isn't necessarily bad- it's just not as good as the go world knows it could be. Whenever you're in a tough situation, try to consider what's par for the situation- either by examining sequences that could lead to a result you're familiar with that originates from another move, or by considering first your weaknesses, second your opponents, and based on the number or magnitude, deciding on a fair and strong outcome. If your opponent played an odd move, considering what's par for the situation can lead you down the road of figuring out how to get a better outcome than could usually be expected. Through this thought, I believe that players will get steadily better by always trying to find the best move, and constantly wondering, "well, what's par for this situation? Now how can I get the advantage?"
Concept number four: "If you can claim territory by forcing your opponent to defend territory worth the same as or less than the territory that you gain by making the threat, then do so." By the same token, when approaching an opponent's stone at the very start of the game, pushing from the outside so that their defensive moves go towards each other, while seeming to give them one side, really becomes an even result if you play with your eyes on the whole board.
Concept number five: "don't forcefully try to save stones that don't have a purpose anymore." This concept can be a little difficult to understand. Primarily it refers to attacking-groups. Once a group is alive, if your attacking stones are in an awkward position (not yet alive themselves, or floating,) attempting to save them can give the opponent a target of attack to gain influence throughout the board and gain a winning situation. Threaten to save them, but also be prepared to make their capture a small, cramped victory for your opponent, should they choose to engulf them.
These are only a few simple things that I'm sure seem obvious to you all, however I believe that if you consider them in earnest, and put honest thought to them during your games, you will get stronger. As always, make sure not to bee too insecure about territory, and keep your fighting spirit burning!
Hopefully this was helpful to some people, and I hope that you'll let me know what you think of it.
Keep eating wisdom,
-Zack