We've tackled this topic before in the past, but it's been a recent FAQ, so we figured we'd share the facts with all those who missed them the first (and second) time around.
As far as your old chips from now-defunct casinos are concerned, we're afraid you're out of luck. When a casino closure is announced, patrons are given an allotted time-frame in which to cash in any chips, TITO vouchers, or winning race and sports tickets they may be holding that have not expired. This extends beyond the end of the casino's life, so often a different casino is assigned the task of cashing in any chips that aren't obsolete once the original property is shuttered.
Under Nevada State Gaming Control Board Regulation 12.070, if a casino is going to close, it's obliged to give fair warning (at least 120 days) to allow holders of its chips to redeem them. Notice of the discontinuance of the chips or tokens and the redemption times and locations must be posted prominently in the casino and published in at least two newspapers of general circulation in Nevada at least twice during each week of the redemption period (check the Legal Announcements section in the Business Section of the Las Vegas Review-Journal, for example.) Once the time's up, however, your chips lose all face value*.
There is some possible good news, however, in that they then potentially start to gain in worth as collectibles among the vast army of chip collectors out there, so you could try doing some googling to get an idea of your "dead" chips' value on a chat room like the Casino Chip and Gaming Token Collectors Club and then sell them direct to a collector or auction them on eBay. You can identify your chips at the ChipGuide.com.
As far as your "live" chips are concerned yes, you'll need to take them to the invidual properties that issued them to you. Casino chips have no monetary value and are just tokens representing their cash equivalent. They are the property of the casino that issued them and while some casinos will accept low-denomination chips from other properties, if you don't then they will still have to return the chip to the casino that issued it, which is a hassle they'd prefer to avoid (see QoD 5/28/2005).
*Note that these rules vary between gaming jurisdictions and the above regulation is specific to Nevada. In Atlantic City, for example, a ruling states that every casino chip must hold its face value indefinitely and always be redeemable, although if the casino that issued it no longer exists, then it must be cashed in with the New Jersey Gaming Control Board.