When you cannot supervise the puppy, he will have accidents that you will not find immediately.  Every time the puppy has an accident that you do not see, it makes it harder for you to make him understand what you want.  You can eventually housebreak a puppy without a crate, but it will take you MUCH longer and will be more stressful on you and the puppy because you WILL get angry and frustrated with him!

When you use a crate for housebreaking, it makes it easy for you to avoid accidents in the house altogether and makes the puppy learn MUCH faster.  If you can do this, he will quickly get the idea that going to the potty OUTSIDE, is what is normal and expected.  If the puppy is allowed to have frequent accidents in your house, he can become confused as to where the proper place to go is.

You can expect some potty training accidents in the crate at first because puppies do not have complete physical control yet.  Do NOT harshly scold or chastise the puppy or older dog for this. 
It is alright to mildly say, " OH! Look what happened here!  You do that outside!" and take the puppy directly outside, even though he may not now have to go. He will quickly get the idea and as his control improves, he will have less and less accidents in the crate.

The idea of using the crate is that while your older dog or puppy is out of the crate, he is to be VERY carefully watched for the first sign that he is looking for a place to go.  When you see this, you scoop the puppy up and take him outside.  When he goes, don't forget to PRAISE him  and do not return him immediately to the house or crate.  Make sure that the reward for going includes praise and some play time!

In the beginning stages of housebreaking, he should ALWAYS be taken out on a leash, even though you may have a fenced yard.  This way, he cannot get easily distracted and run off to play.  He can concentrate more on the job at hand.  You should choose a word to tell him what you want,
( go pee, go potty, ect.) and he will eventually learn to go on your command.

Teaching your puppy or older dog to go on lead in your presence is valuable for several reasons.  First of all, if he is comfortable going in your presence, he will not be as likely to try and sneak away to go in private.  Secondly, it makes traveling with your dog much easier.  Dogs who are never taken to the bathroom on lead are uncomfortable doing so and will often have to be walked endlessly to get them to go.    This point will be driven painfully home as you walk round and round your hotel parking lot, thinking longingly of the comfortable warm, ( or cool) room waiting for you!

Your puppy can be out of the crate to be with you for play sessions, or while you are watching TV or any other activity that you can do and still observer your puppy.  If you are doing something that will occupy your full attention, and you cannot watch him......he should be returned to the crate.  This way, you should be able to prevent most accidents from occurring at all!  If you are diligent and
consistent, you may in some cases not have to do this for longer than a few weeks.