I've used both FLEXlm from Macrovision (formerly Globetrotter) and the newer RLM from Reprise Software (as I understand, written by FlexLM's original authors). Both can key off either the MAC address or a physical dongle, can be either node-locked (tied to one machine only) or "floating" (any authorized machine on the network can get a license doled out by a central license server, up to a maximum number of simultaneously checked-out copies determined by how much they've paid for). There are a variety of flexible ways to set it up, including expiration dates, individual sub-licensed features, etc. Integration into an application is not very difficult. These are just the two I've used, I'm sure there are others that do the job just as well.
These programs are easily cracked, meaning that there are known exploits that let people either bypass the security of your application that uses them, either by cutting their own licenses to spoof the license server, or by merely patching your binary to bypass the license check (essentially replacing the subroutine call to their library with code that just says "return 'true'". It's more complicated than that, but that's what it mostly boils down to. You'll see cracked versions of your product posted to various Warez sites. It can be very frustrating and demoralizing, all the more so because they're often interested in cracking for cracking sake, and don't even have any use for your product or knowledge of what to do with it. (This is obvious if you have a sufficiently specialized program.)
Because of this, some people will say you should write your own, maybe even change the encryption scheme frequently. But I disagree. It's true that rolling your own means that known exploits against FLEXlm or RLM won't instantly work for your application. However, unless you are a total expert on this kind of security (which clearly you aren't or you wouldn't be asking the question), it's highly likely that in your inexperience you will end up writing a much less secure and more crackable scheme than the market leaders (weak as they may be).
The other reason not to roll your own is simply that it's an endless cat and mouse game. It's better for your customers and your sales to put minimal effort into license security and spend that time debugging or adding features. You need to come to grips with the licensing scheme as merely "keeping honest people honest", but not preventing determined cracking. Accept that the crackers wouldn't have paid for the software anyway.
Not everybody can take this kind of zen attitude. Some people can't sleep at night knowing that somebody somewhere is getting something for nothing. But try to learn to deal with it. You can't stop the pirates, but you can balance your time/effort/expense trying to stop all piracy versus making your product better for users. Remember, sometimes the most pirated applications are also the most popular and profitable. Good luck and sleep well.