I do not seem to improve

For quite some time my rating was around 1250. I sometimes win and get up to 1300 or slightly more but eventually I fall down to around 1250.

Why do I not improve? Is there some level the player can reach after which he cannot improve anymore? Or is there some aspect that I need to focus on more?

Or is it just that I need to play more games?

What way would be the best to improve at my level?

Usually to improve, you need to learn chess stuff.

The thing holding most people back at that level is inattentiveness to their opponents' tactics.  Look for the other's guys tactics as well as yours.  If you find a good move, find a better move.  Look at all checks, captures and threats...for both sides.  These are all ways of saying...be more careful.

If you've been playing a lot of bullet or blitz, play longer games so you have the time to exercise care.

Finally, continually drill yourself on tactics so you can commit them to long-term memory and can instantly recognize them over the board. As I've said elsewhere, I recommend doing the same sets of tactics over and over again. The repetition really helps with pattern recognition.

To put it another way, what's probably holding you back is your thought process, and not any lack of knowledge of openings or strategy or all that other good stuff you would find in many chess books.

So work on thinking more systemically and exercising greater care.  And if you're going to crack open a book, crack open a book on chess tactics.  Better yet, get yourself of copy of CT-Art, software that can drill you on tactics.

Thank you for your reply. It seems that tactics are what I should focus on to improve my chess level.

Yes, tactics, and looking for tactics for both black and white on every move.

A 1200-player's problem could be as simple as he's looking for the other guy's tactics on MOST moves, but when he thinks he sees a really really good tactic for himself, in the excitement of the moment, he neglects to CAREFULLY look for his opponent's best response.  So you may be taking care to look for the other guy's tactics in 39 out of 40 moves, but if you neglect just one move you may well lose the game.  

 I remeber that when I was that rating, I would usually forget to attack weakly defended pieces because I`d get too focused on the center of the board

Perhaps you should study opening, tatics ext.

http://www.chess.com/forum/view/general/improvement-in-chess-according-to-elo

http://www.wikihow.com/Become-a-Better-Chess-Player

I've always said to my little brother - whom I've been teaching chess - that when he calculates, he should think about defense before attack. That corrosponds well to what yyoochess said - pay attention fully to what your opponent's doing.

Try to study each of your games.  I see you have played 333 live standard games here on chess.com.  Perhaps you should analyze each of these. A productive goal would be to look for one, two, or three things from each game to take some learning from.  Keep your learnings in a notebook or electronic file that you can continually review and revise.  In time, you will begin to recognize more and more patterns that will help you both seize opportunities and avoid mistakes.  

+1 on the game analyses to learn from your mistakes.  People get stuck in a rut when they make the same mistakes over and over again.  I've read that it's best to go over your games first without the aid of a computer, and then check your analysis with a computer.  I've also read that Caruana has been keen on learning from his mistakes since he was very little.  You too can start 7-0 in a supergrandmaster event one day.

When you analyze, think about the move, but think too about the thought process that led you to that error.  Did you rush?  Did you forget to look deeply for your opponent's threats?  Were you focused too much on one part of the board?

SchriSchri gave some great advice. I've been essentially doing that for the past two years, and I have steadily improved. At least, I believe I have steadily improved. Guess I won't really know until I begin playing in tournaments again.

I keep a "Chess Log." It's 62 pages long now. At the very least, I've been able to pinpoint and identify the bad chess habits I have in order to combat them.

I looked at your games, and yes, tactics will certainly help.  However, you are also in need of some very basic positional and strategy guidance.  I'm sure you have heard "develop your pieces first" "dont move the same piece twice in the opening" and "be careful moving the pawns in front of your king before you castle" but you are actually violating these principles fairly routinely.  

While you have played a lot of 30/30 games here on chess.com, it is obvious you havent really had anyone decent to help you and provide guidance.  You need to spend a bit less time playing, and a bit more time getting guidance.  If you dont have a live person that can do this with you, post some of your losses in the analysis forum and ask for help.  

None of this is a knock on you.  I think it is very difficult to improve simply by playing a lot of games with no one to give guidance at all.  If you were playing this many live games, you could chat with your opponents and maybe pick some things up.  In the internet age, I think its just tough to get better merely by playing faceless opponents.  

Your in a rut basically.  You will never break out by doing what you are doing -- playing a lot of games without obtaining feedback and guidance -- but there is definitely easy improvement to be had if you can get guidance.  

Eat a healthy diet and get plenty of rest.

True Mark.  However, not making moves like 8. ... g5 is easy to learn and will make a difference as well.  If you look at the number of games he has played, its clear that he isnt absorbing basic strategy just by playing.  I dont think that is a shock, I think most people need some guidance, and he hasnt gotten it yet.  

Gamesfan, g5 violated several basic beginner principles.  First, you made yet another pawn move without developing a piece.  Look at how few pieces you have developed and how many pawns you have moved.  Develop - take your pieces out - first is a basic beginner rule.  Second, you havent castled yet, and g5 and f5 create a lot of air in front of your king -- they are what we call weakening.  To the extent your planning on castling queenside, ok, but its still not a good idea to weaken your kings protection so much before doing it.  Here it seems harmless, but at your level danger can and will strike out of the blue when you make moves like this.  

I'm not quite at that level of play yet, but I have improved quickly, and I find i helpful just to segratate your focus on parts of the game. I might spend a few days on openings only, then on middle game, then on end game. After that I go back to the board and usually go up a little each time.

I also will only do tactics trainer for a few days to see if I can separate it all out. Focus on a few little things, then focus on putting it all together later.

Simply playing chess will not necessarily improve your game if you don't do anything else. It's like learning to play any game. The more time and effort you put into it the better you become. Study openings, two for white and two for black. Learn them well enough to be comfortable playing them. Play other players that are better than you by at least 1000 point. use the tactics training on this site. It is very helpful. do an analysis of each of your games. Learn from your mistakes.

try something different if the same old thing is not working!

First, if you are playing fast paced games, maybe try playing a SINGLE slow game, that is get one game that you focus all your mind on, with more than a day to choose each move.  Then spend time making that move --- actually make the move on the analysis board and then try to find the best move for your opponent, do that a few moves deep, see if your initial move is actually any good or if it drops a piece. 

also, do your daily tactics trainer.  On those, forget the score and see if you can just solve the puzzles correctly.   Speed comes with time and practice, in both situations. 

If the above game is "typical" then you need to study a few basic openings and more importantly, just the opening concepts of development and pawn structure. 

Some things you can learn by doing.  Some things have to be taught.  Some things take a lot of effort to learn.   Yes, you have limits, but odds are you have not reached them.  And its not a hard limit -- even after you peak, and seem to hit a limit, sometime later you may break through it and progress again.    

Some study and effort will be required.  But keep it fun.  You DO have limits and odd are your limits are "below the money"  --- meaning you are unlikely to be able to make a career of playing the game with match winnings and sponsorships etc.   Only a few people get that good.  Until you find yourself getting closer to that level of play, remember to have fun and just enjoy it -- don't let it become a chore that you hate. 

As others have said, a 1250 should definitely learn and exercise basic opening principles and simple strategic ideas.  But, as folks have also pointed out, serious opening study or strategic study is not needed.  Tactics and blunder checking are the priority.

I forgot who said this, but a famous chess coach pointed out that a computer with perfect strategic knowledge that looked 2 moves ahead will almost always lose to a computer with no strategic knowledge that looked 3 moves ahead.