It's not possible to win without taking cards (unless you have a very cooperative opponent!), so the trick is to be judicious about what you take. Getting a high-value card isn't the end of the game for you: if you can take most of the chips in the process, you can still come out ahead.
You usually don't want to simply pick up a card with no chips on it. Your opponents generally don't want the cards you want, so it's worthwhile to send a high-value card around a couple times before you pick it up, even if the card would be part of a run for you. Of course, if it would also benefit an opponent, make sure you take it first!
Try to keep a rough idea of how many chips your opponents have. Don't get so greedy for chips that you accidentally force an opponent to take a card you really need!