In my experience the typical, established clubs are well-equipped for events with boards and pieces, but bring your own clock or hope your opponents will.
Non-club affiliated tournaments, be prepared with pieces and a board and a clock or hope the opponents are carrying.
I know it's different in Europe; it's been discussed a few times before.
edit: in my first tournaments the organizer provided boards and pieces for all 50-60 boards. Your mileage may vary.
Thank you for your answers!
Very interesting indeed. Normally in my city if there are big events clubs supply the material together and if there isn't enough the Royal Dutch Chess Association has material that can be hired for a low fee.
YES, although I'm so old I actually played in tnmts where paper boards, bottom-of-the-line plastic sets (and clocks too? can't remember) were provided by Bill Goichberg, a very selfless TD and USCF official - but this was back in the 1960's!
Nowadays you better bring everything you need to a US Chess tnmt. I recommend getting a section of PCV pipe the right length/diameter with caps on both ends for carrying your roll-up board in, they also double as self-defense weapons in bad neighborhoods (which occasionally host chess tnmts, at least here in the US)
25 years of tourney chess for me in the US and I always took my pieces/clock/board,scorebook and a reliable pen...... Most players did in fact as the equipment was rarely ever furnished. I played all my US chess in the US Southeast. I guess really big events, like the world open, may have furnished stuff but they never did in my neck of the woods... 
Then I moved to Europe and did it the other way.... they furnish almost everything here , even pens/pencils very often ! The down side to this is that many playing venuse I have played in here dont have central air and heat so you may be shivering through all your games or about to pass out from the heat. I have also had problems here I never experienced in the US...... no toilet tissue in the restrooms ! ( and sometimes these were pretty nasty ) So.... you dont have to bring your own pieces, clock and board but you might be wise to bring a roll of TP with you...... just in case.
Its odd but the very best conditions I have played in, as well as the very worst, have been here in Europe.
25 years of tourney chess for me in the US and I always took my pieces/clock/board,scorebook and a reliable pen...... Most players did in fact as the equipment was rarely ever furnished. I played all my US chess in the US Southeast. I guess really big events, like the world open, may have furnished stuff but they never did in my neck of the woods...
Then I moved to Europe and did it the other way.... they furnish almost everything here , even pens/pencils very often ! The down side to this is that many playing venuse I have played in here dont have central air and heat so you may be shivering through all your games or about to pass out from the heat. I have also had problems here I never experienced in the US...... no toilet tissue in the restrooms ! ( and sometimes these were pretty nasty ) So.... you dont have to bring your own pieces, clock and board but you might be wise to bring a roll of TP with you...... just in case.
I guess that really in quite different in other countries. Europa isn't a union like America but different nation with very different cultures.
In which country do you live?
I always see things like "Tournament bags" coming by in American web shops. Do you need to bring your own material to chess tournaments/clubs in America?