Best practice for an endless/ periodic execution of code in C#

There isn't necessarily a "best way" to write long-running event processing code. It depends on what kind of application you are developing.

The first example you show is the idiomatic way in which you would often see the main method of a long-running thread written. While it's generally desirable to use a mutex or waitable event synchronization primitive rather than a call to Sleep() - it is otherwise a typical pattern used to implement event processing loops. The benefit of this approach is that it allows specialized processing to run on a separate thread - allowing your application's main thread to perform other tasks or remain responsive to user input. The downside of this approach is that it may require the use of memory barriers (such as locks) to ensure that shared resources are not corrupted. It also makes it more difficult to update your UI, since you must generally marshal such calls back to the UI thread.

The second approach is often used as well - particularly in systems that already have an event-drive API such as WinForms, WPF, or Silverlight. Using a timer object or Idle event is the typical manner in which periodic background checks can be made if there is no user-initiated event that triggers your processing. The benefit here is that it's easy to interact and update user interface objects (since they are directly accessible from the same thread) and it's mitigates the need for locks and mutexes to protected data. One potential downside of this approach is if the processing that must be performed is time-consuming it can make your application unresponsive to user input.

If you are not writing applications that have a user interface (such as services) then the first form is used much more often.

As an aside ... when possible, it's better to use a synchronization object like an EventWaitHandle or Semaphore to signal when work is available to be processed. This allows you to avoid using Thread.Sleep and/or Timer objects. It reduces the average latency between when work is available to be performed and when event processing code is triggered, and it minimizes the overhead of using background threads, since they can be more efficiently scheduled by the runtime environment and won't consume any CPU cycles until there's work to do.

It's also worth mentioning that if the processing you do is in response to communications with external sources (MessageQueues, HTTP, TCP, etc) you can use technologies like WCF to provide the skeleton of your event handling code. WCF provides base classes that make it substantially easier to implement both Client and Server systems that asynchronously respond to communication event activity.

If you have a look at Reactive Extensions, it provides an elegant way of doing this using the observable pattern.

var timer = Observable.Interval(Timespan.FromMilliseconds(100));
timer.Subscribe(tick => OnSomeCondition());

A nice thing about observables is the ability to compose and combine further observables from existing ones, and even use LINQ expressions to create new ones. For example, if you wanted to have a second timer that was in sync with the first, but only triggering every 1 second, you could say

var seconds = from tick in timer where tick % 10 == 0 select tick;
seconds.Subscribe(tick => OnSomeOtherCondition());

By the way, Thread.Sleep is probably never a good idea.

A basic problem with Thread.Sleep that people are usually not aware of, is that the internal implementation of Thread.Sleep does not pump STA messages. The best and easiest alternative, if you have to wait a given time and can't use a kernel sync object, is to replace Thread.Sleep with Thread.Join on the current thread, with the wanted timeout. Thread.Join will behave the same, i.e. the thread would wait the wanted time, but in the meantime STA objects will be pumped.

Why this is important (some detailed explanatiopn follows)?

Sometimes, without you even knowing, one of your threads may have created an STA COM object. (For example this sometimes happens behind the scenes when you use Shell APIs). Now suppose a thread of yours has created an STA COM object, and is now in a call to Thread.Sleep. If at sometime the COM object has to be deleted (which can happen at an unexpected time by the GC), then the Finalizer thread will try calling the object's distruvtor. This call will be marshalled to the object's STA thread, which will be blocked.

Now, in fact, you will have a blocked Finalizer thread. In this situations objects can't be freed from memory, and bad things will follow.

So the bottom line: Thread.Sleep=bad. Thread.Join=reasonable alternative.