Crows are among the most intelligent and adaptable birds in our yards and neighborhoods. Crows (along with jays) descended from Australian ancestors that moved north and apparently first evolved in Asia millions of years ago, and have since migrated across the world split into many different species. All crows have a unique ability to solve problems, and some even use tools—perhaps you've seen the video of New Caledonian Crow using a tool to get food on youtube.
So what do you do when one of these incredibly smart birds figures out that your house or yard provides something it wants and starts becoming a nuisance? Perhaps they have learned that they can tear into your garbage bags to get rotten goodies, or that there may be bugs on your roof? At that point crows go from being amazing creatures for us to admire, into a problem for you and your property.
First it is important to realize that you probably are not dealing with just one individual rogue crow. Crows usually live in family groups that include parents, young birds hatched that year, and sometimes older helper siblings or other relatives. Crows are also territorial, so this family group living in your neighborhood really are your neighbors. They aren't going anywhere, so you have to deal with them with this in mind.
Bird sonic devices can work to keep crows away temporarily, but may not work to address the daily movements and actions of your local family of crows. Your local crow family will be very smart about figuring out what are real threats and not real threats in their territory, so it is usually only a matter of time before they figure out if a sonic system or other deterrent really isn't a threat. The same thing holds true for visual deterrents that might scare the crows initially, but may not work over the long term.
To keep crows from being a problem in your yard, try to figure out what it is that the birds are attracted to and try to get rid of that. If the birds are ripping into your garbage bags, see if you can use a garbage dumpster or bin that the birds can't open. If crows are picking at your roof, it may indicate that you already have a hole up there that the crows have spotted and are now pecking at to see if there are bugs underneath. So get your roof checked and fixed.
If you can't figure out what the birds are being attracted to, or otherwise can't get rid of what the crows are coming to, you may be able to keep the birds away with some psychological warfare—some folks have luck deterring crows by getting a fake crow from a craft, holiday (Halloween), or costume store and hanging it upside down with wings extended as if it were dead. That is a kind of macabre anti-crow terrorism tactic, but it sometimes works to scare the crows away.
If these suggestions don't work, or if you just want to learn more about your neighborhood crows, here are some additional online resources:
http://www.humanesociety.org/animals/crows/tips/solving_problems_crows.html
http://icwdm.org/handbook/birds/AmericanCrows.asp
http://www.absolutebirdcontrol.com/bird-types/american-crow
Do your homework, read up on your crow neighbors, and do what you have to so that you can be a good neighbor to your local crow family while protecting your property.