I personally find there are more negatives than positives in playing rated games and in fact have stopped playing them for that reason. I feel they detract from the enjoyment of the game, making the pursuit of the almighty point its main purpose rather than trying to create something esthetically pleasing at the possible risk of losing. When I played rated games, my sole purpose became to avoid losing and having my rating drop, changing the way I played. Why was it decided to have such a system in the first place? Wasn't playing the game for it's own enjoyment and mental challenge sufficient motivation?
A rating system has many advantages:
- Ensure that you play against opponents of similar ability, especially in tournaments and/or leagues. Most people enjoy a challenge most when it is hard but not impossible.
- When you do happen to play against someone of far stronger ability, most rating systems make provision by not penalising you too much when you lose (and similarly not benefiting you too much when you beat a much weaker opponent). I find this encourages me to enter tournaments in a higher category when I'm up for a challenge, because I know that mediocre results won't necessarily destroy my rating.
- Provides an objective measure of improvement. I find it interesting to see how my rating changes over time, and obviously I feel very satisfied if it increases after hard work.
As for negatives, I can't think of many:
- no rating system is perfect, and there is always a bit of dispute about how much they reflect actual playing ability. This is not really a problem as most players know that their rating is really just an approximation rather than the absolute indisputable measure of their strength.
- I know some players "manage" their rating, often losing games to prevent it from going too high, so that they can play in lower-graded sections of tournaments. I don't care much for these people, and fortunately there are not many of them. As an interesting note here, the opposite also happens - strong players sometimes refuse to play in tournaments if there are not many players of similar strength. For example, Nakamura stopped playing in the US Championship for a number of years because he believed playing against weaker opponents would have a detrimental affect on his rating (he wants to stay in the 2800 club you see). Luckily for us chess fans he seems to have gotten over this particular affliction because he played this year and won.
Try not to take ratings too seriously - it serves its purpose well enough.
The rating system is a means of ranking players. The question you are asking therefore is really about the motivation behind ranking players; apart from the usual reasons (which country has the best players, who is the best player, etc.), national federations need some criteria to decide which players to send to international tournaments (say the olympiad).
While it is possible to select players that win the national championship (and this is common practice for many countries), it is unfair to have an entire national team composed of players selected from a single tournament (where attendance may not have been possible for some who have been performing well throughout the year, and when there is a large pool of players and not enough rounds, the rankings of runners-up are not very convincing); a ranking system is needed as another decision criteria, at least for the playoffs.
Rankings are an integral part of any competitive game or sport; the big question now is how effective the current rating system is, in the sense of how it reflects on players strength.
As for playing in tournaments, if whether a game is rated or not affects your approach to the current game, resulting in you trying harder "not to lose", perhaps it shows that indeed rating systems encourage you to play better.