There are a few domains I have an eye on. Right now, someone else owns those domains, but doesn't actively use them. Is there a service (if possible provided by one of the major registrar), that I can use to put myself on standby for a domain? I.e. the service would register the domain for me as soon as it becomes available?
One of the biggest firms for getting expiring domains is SnapNames.com. I think the price is something like $59 and they'll provide you with a "SnapBack" on the domain name of your choice.
SnapNames has partnered with a large number of registrars (both large and small) to help boost their chance of success. They attempt to register domain names with SnapBacks placed on them at the exact second that they become available.
Since they get more "tries" than you do... their chance of success over someone trying to manually grab a domain is MUCH greater.
I've used them in the past to get names for clients who forgot to renew and almost lost the domains.
Keep in mind that you're basically purchasing the CHANCE of getting a domain name. They are partnered all over so they have a very high success rate but its NOT 100% guaranteed success.
That being said... these guys are probably your best bet if you're serious about getting the domain name.
As KPWINC mentioned, SnapNames is great. Another one to keep in mind would be NameJet.
If the name you are looking it is of any value, it will probably be sold through a premium partner agreement rather than just deleted where it can be picked up by any drop catcher. These names become available through partner agreements approximately 35 days after expiration. If they are not purchased during a partner auction, they will be deleted approximately 78 days after expiration. When they are deleted, any drop catcher can "catch" the name for you.
Network Solutions, Enom, and some Fabulous domains will first become available at NameJet. Moniker, Dotster, Register.com, and many others will first become available through SnapNames. Finally, some registrars do not have partner agreements and therefore their names will only become available after deletion.
Also keep in mind that just because a name doesn't have a website that it is not necessarily unused. Many people will have a great domain name and only use it for email.