One of the most effective ways to tighten your writing is to eliminate thought verbs and sense verbs--the little filter words that provide an extra layer between your character and the reader. Sometimes these words are necessary, but most of the time cutting them will strengthen your writing, making it less wordy and less passive, without changing the meaning.
Here's a list of some of the culprits: felt, think, know, understand, realize, believe, want, remember, imagine, desire, wonder, watch, look, see, hear, listen, notice, spot, figure, seem.
Also watch out for these empty words: start to, begin to, that, just, really, well.
Change: I watched the girl start to walk across the room.
To: The girl walked across the room.
Or even better: The girl crossed the room.
If you can cut a word/phrase without changing the meaning, you should cut it. Check out this great post by Cheryl Klein for more examples.
And if you can't simply cut the thought verb because it's the only verb in the sentence (something like, "I felt happy"), the sentence should probably be revised anyway. Writers are always told to show instead of tell, and unpacking the sentence as Chuck Palahniuk describes in this post is a great way to do that.