Should i go on a trip with out my boyfriend?

of course.... he's a losr in the first place. Besides, when you get back if he's real happy to see you then you know he missed you and he'll be there for you

Sure, as long as you two have complete faith and trust in each other.

Why not? Unless you're planning on cheating on him or something, I don't see anything wrong with taking a trip without your significant other if he can't come due to work/school/money etc.

Gotta go with aslongasitrocks.

This will depend on what your trip is about. It may be your bonding with some friends that does not involve him, family trip which may not fit him in, etc. By all means, go without him. He should understand as long as you 2 are comfortable with this.
If you want some personal space, also a good idea to go alone. If you think you cannot be yourself when he goes along, go alone for yourself.
Whatever your reason to do so, it has to be your own choosing. And you know he consequences and are willing to face them.

Of course you should.

Last year, I travelled from Melbourne to LA (USA) for 8 days with out my husband and children.

Just because you are a couple doesn't mean you loose your individuality. If you want to travel and he doesn't then say "See you when I get back honey" or "will you drive me to the airport?"