How is it possible to avoid cliches in storylines that you are writing? Obviously, there are external sources of influences as you read more and more. It would be possible that we are subconsciously and unaware that we are crafting a story that bears similar resemblance to a story that we particularly like.
Layered, nuanced characters and depth of story will help you avoid cliches.
Look, we're all writing a lot of the same stuff. Good guys, bad guys, boy meets girl, she gets kidnapped, blah blah blah.
Cliche's arise when: 1) the characters behave in a certain way without the proper background. 2) They only behave this certain way
Hank, the grizzled veteran cop who is a drunk and is just waiting to get his twenty years so he can retire... that is right out of the cliche book. But, if your story outlines why Hank is the way he is, and also gives him more dimension, then Hank is no longer a cliche. Hank becomes a real character. Making Hank a drunk cop is great, but maybe he's into racquetball or model trains or something. Nobody in life is just one way. Your characters shouldn't be either. If you can make Hank's recreational racquetball somehow figure into the story so that Hank can overcome his obstacles and save the day, well, good times!
On the flip side, you can't go giving every character extensive background intros and laundry lists of interests. This is the art, finding the middle ground between shallow characters and boring your reader to death. The best do it so well that you don't even notice. The worst, well, I'm sure you can think of some examples.
Cliche characters lack depth. Come up with strong motivations, fears, desires, etc... and think about the implications to the character's behavior due to these factors. Don't write the perfect "good guy" or the purely evil "bad guy." Make them interesting. Give the character an unusual trait/history, and make it important to the story.
Cliche themes shift with the zeitgeist. Vampire movies/stories have become cliche, thanks to Twilight. Zombies are cliche as well. If you're going to write for one of these genres and want to avoid being cliche, approach the story from a fresh angle. Sean of the Dead (zombie/rom-com) and Zombieland (zombie/coming-of-age) are examples.
Keep in mind that cliche stories can be successful. See Avatar. It's Dances with Wolves set in space, with fairly shallow characters and a predictable ending.
Don't try to avoid clichés just for the sake of avoiding them - no matter how original you think your idea is, some reader somewhere will see it coming from a mile away. Instead, try to make people give a darn.
My favourite example of this is in video game design: you can have a character X asking players deliver an item Y to location Z. The player may initially go "yawn, it's a bloody FedEx quest." There's two major schools of design here: Make the video game full of boring delivery quests where nothing of interest happens (you get points while having boring old time! Whee!) or make a few delivery quests where interesting things take place, and the player can see that you didn't just rev up the automatic quest generation wizard built in the game editor. It's still a FedEx quest, but people actually had fun playing it, so they won't really complain. Mission accomplished.
So, if your fascinating plotline is mercilessly picked apart by nitpickers in TVTropes, that's not a bad thing - it happens to everyone and every story. The bad thing is when all of the readers yawn in unison and join the aforementioned TVTropes nitpickery because they know all about your story without even reading it.
Find a good editor, and when you hand over the manuscript, let the editor know that this is a particular issue for you, and ask the editor to keep an eye out for it. If you know that you read a lot of one writer, mention that writer to the editor and say "I like this person, but I want to make sure I'm not unduly influenced."
There's a reason you can't really "proofread yourself." It's very hard to see your own biases.
TV Tropes is a good resource for looking up clichés in literature as well as other media.
As has been said, depth and variety can turn a cliché into something engaging.
What's interesting is the way some writers use clichés to their advantage. It happens more in television than other forms -- and it happens in ensemble cast shows more than other television. If there will be depth added in later episodes, the audience needs to get through the first hour (the pilot) without a huge amount of background. Clichés become a sort of shorthand for introducing characters and even plot elements.
The spoiled rich girl may have deeper layers to her, but in the early part of the story she's only needed as a comic annoyance when paired against the hero. She may come off as a cliché at first, to be given depth when her part of the story comes along.
Hank, the drunk burn-out cop mentioned by gmoore, may not become a "real character" until the reader has accepted him as a cliché and moved on.
The most skillful writer will introduce a quirk or two for every character so that even secondary characters never seem like clichés.
A renowned songwriter and artist from my country, Juan Luis Guerra, states he listens continuously to all the music on the media; he says it helps him avoid doing the same thing everyone else is doing.
The extrapolated advice seems to be: Read a lot, aware of what you're doing. When you write, you'll know what to avoid. If you don't read the clichés and get to know them, you won't know to avoid them.