Yes you should try and play most of your games against players of least similar rating if that equates to similar ability, however both of you to get where you are now:
45 games
Current: 1981
Avg. Opp.: 1656
Earlengray
77 games
Current: 1927
Avg. Opp.: 1629
@Darthstapler8: "strong" is relative. The point is - let's play against a people who are of your own league! If your rating is 1500, you probably can easy win agaist somebody who is 1000, as like I can beat somebody who is 1500 (and 2500 can beat me), but there are no much enjoyment in it. I could enjoy more if a gain 60% against peple of my league, then 100% against beginers.
@Darthstapler8: I understand it. I wiil play as it maybe when I gain more experience. I also wrote a few articles with analysis which can be of interest to learn. I am going to post my game against WGM RusudanGoletiani. I lost, and it is a fine example of balte for the center! And look An interesting queens endgame!
I agree on this also. I also accept when they challenge me, it would be rude not to do that. But that was not what this topic was about, I think. It was about those people who only play against weak opponents and avoid to play against those of similar rating so that they can have big score and percentage win. That is rare in my experience but it does happen.
I definitely agree that it's more fun to win when the contest is between people who are well matched.
Am I the only one who see's this - LydiaBlond said "I like to test myself agaist my equall or better -"
Can you all see what I see.
She does not like to play people lower...Hmmm
People lower than you might want to play you because of the same reason you want to play someone higher than you. You do not want to play the lower person but you want someone higher than you to play you, the lower person.
lettherebechess - great point. Personally, I enjoy playing people of wide abilities - although admittedly I haven't played too many players who are way better than me (and there are MANY people in that category!).
@Gonnosuke: Yor rank is much higher then mine, and you play more games - so you have less choices. You play a game against me, -350 points - however, I suppose, you also have some kind of lower limit, -500 or so.
I analysed a list of players here. It is a pyramid at the top. There are 57 players with 2300 points or more, and 774 with 1900 or more.
@Gert-Jan: In general, rating-points calculated in Elo or Glicko system are a good measure of player's real strength, if you have at least about 20 games concluded and it was not years ago. (Less games - can't be sure. I was recently challenged from a beginer here, no completed games, 1200 points - I politely decline, he need to start with lower-ranked people, as I did. Well, I was lucky enough to win my first game here in 30 minutes, it was a mate in 8 
and my rating improved from 1200 to 1410. After two days i had 9 games completed, +8-1, and 1753 rating points.)
My real strength is around 2000, it can fluctuate +100 or -100; of course, I try to improve my game and my result: games which I lost teach me abot important weaknesses in my play. +/-200 indicated a real diference in power! I hope to achieve 2200 one day!
@LetThereBeChess: You do not want to play the lower person but you want someone higher than you to play you, the lower person.
Yes. I don't see a problem. 
An definitely - not a "lower person", only less sucessfull in playing chess on-line! 
I TOTALLY AGREE!! I've been playing weaker players for years now, in my school chess club, which is really horrible, because ever since last year I've become the highest rated player there, and I'm not improving at all. It not only hurts your ratings, it's not satisfactory, because it's expected, because if you lose it's a total disaster.
My favourite range of players are my rating and at most 200 points more, so I can improve and keep pace with my own standard, knowing that if I fall short it's room for improvement and not a serious blunder (though it could be). And if I win, I'll know, keep the good work up, you're improving. And this you don't get playing weaker players
I have a reason for not playing members lower rated then me. You see, I got to where I am today by playing members much higher rated then me, losing several games in a row, learning and then kicking their buts when I achieved their level. This caused my rating to surge dramatically.
So now I'm afraid of others doing the same to me.
It looks obvious to me that lydiablonde's statement is being misinterpreted by some. In context it is clear that she means she doen't play people say 400 points below her. As she is 2000+ here that makes sense. But here 2000+ playing 2430 say does make sense. You see, a difference of 100 points (whether on chess.com scale, fide scale or whichever) at approx. fide 1100 say, is *much* bigger than a difference of 100 points at fide 2400.
Something needs to be stated here... people can make their own decisions who to play and for what reason. It is wrong for anyone to tell anyone else who they should be playing and for what reasons.
There are people on this site who simply want to play some fun games, they don't care about how good they get or where their rating is.
I do try to get better, but it is not some all-encompassing passion that drives me and will dictate who i play and who i don't play.
I am the first to admit my rating is a bit inflated. I have many friends who are learning the game of chess, and many friends who have learned but haven't played as long as i have. Some people have told me my games with them should then be unrated as it inflates my rating.
Who's business is it how accurate my rating is or how i play my games. I don't mind someone who says they don't play lower rated players, but telling others that they shouldn't because "we need to be able to trust people's ratings" is really stupid.
When I say it's stupid, I'm not calling anybody in particular stupid, because i'm not sure that is actually anyone's intention here... but in case it is.. then YES.. i'm calling you stupid! 
Play your games and who you will, and leave others to play who and how they will.
And if anyone wants a nice boost to their rating points (if you care that much)... my rating is inflated... i'm definitely NOT as good as others rated the same as me.
Bon Appetit
my rating hasnt settled in - it was like changing from fahrenheit to a new scale for which i didnt know even a rough conversion formula - i now see from games that i would be 1700-1750. So at present i am playing ppl much weaker than me [1350+ drops a piece on move 5 in a 7 days/move game, then 1600+ drops a piece within move 10 or so in a 3-day/move game... to simple forks!]
MY ratings will always be inflated. Reason: most of the time i will not be playing more than 6 games a time, all with at least a week/move, and at least 3 with 10 or more days / move. [if there was the option of a month a move i could take on more games...] Since almost everyone here plays a lot more games simultaneously, and since i am retired and moneywise secure, I'll have a lot more time to pursue my other interests (no chess-monotony) - chess is one of my top priorities - 9th or so - so i can analyse games at leisure! Plus I am 47, have been successful in various [academic] fields, so i have nothing to prove, taking the tension off me. Fact of life.
Don't you think all this - specially my playing fewer games / day will inflate my rating to 1800+ in 6 months, whereas i should be i think 1750 [i have no desire to improve much further - if improvement comes it is fine with me - advantage of being 40+ and nonconsumerist.
UPDATE: my rating is already 1812 as of june 11, 2008.:) [of course i am not ranked - rating-deviation still too high, only 8 games completed]
I present all this as a case study. Here unlike in tennis you don't lose ratings by low playing frequency, it is just that your RD increases.
There could be other resons why other people's ratings would be inflated. [i dont mean with cheating :) ]
Glicko is within the bayesian paradigm - priors, cox's theorem and all, so speaking of probability while correct could be misleading as most people [except bayesians and physicists] only know of the more conventional probability [from fics you can get the link to the glicko paper - i had it on my HD which crashed - i am yet to put back everything from backup) - in a few minutes i'll give you the link - it is not *quite* R1/(R1+R2) -
In fact it is designed so that playing lower-rated ppl only will *not* inflate your rating - so Vance, ignore those calumnies against you - they are simply false though in most cases not deliberately, because they haven't read up the rationale of glicko ratings. Next post, i'll give everyone interested the link. [the link at fics "help glicko"doesnt work]
I published it on my blog. I submit it here too, for I like to see come coments.
I see some people, with not so high rating, has an excelent score, without or very few defeats. They play a lot of games agaist people with much smaller rating.
However, I don't think it's interesting to reproduce wins agaist much weekers. It's as a boxer of heavy category enjoy beating much smaller. I like to test myself agaist my equall or better - it means, players with at least 1800 rating points.
At the moment, I play 17 games (8 in a tournament). Average rating of my oponents is 1952. And there are thought batles - no more easy wins! Two days ago I achieved my first win agaist a player with rtg beter thet mine, LydiaBlonde vs mydarlingron I published this game in forum: Don't play a Steintz's variation!