* Playing Cue (w/ two-three shafts, just in case you find yourself in a situation where you need a new shaft, like your tip flies off - I often carry two-shafts with my favorite tip and one shaft with a tip i'm experimenting with - sometimes I carry a different type of shaft with me depending on my game).
* Break Cue (I carry two break cue shafts with me, one with a Phenolic Tip and one with a Hard Leather Tip - some tournaments have banned the use of a Phenolic Tip to protect ball condition - last thing you want is to be in a competition that doesn't allow Phenolic Tips and then realize that you don't have any other tip, at that point, you've lost your break cue).
* Jump Cue (I find these to be unnecessary in my game, but, that's not to say you'll never need it! There will be times when you have no other shot but a Jump Shot, and you'll be thanking yourself for bringing one in the heat of the moment. Something you MUST have with you, even if you don't use it.)
* Tip Shaper/ Scuffer (This is an absolute necessity. I do not know anyone who doesn't go around without one of these. I carry two with me, a Cuetec Bowtie and a Cue Cube. I guarantee there will be a time when you will use this. I use it after every miscue.)
* Tip-Pik (If you don't have a shaper/scuffer with a built in tip pick, then you'd want to pick up a separate one. Tip picks are important to pierce holes in the leather tip to allow chalk to adhere well. However, with the development of Blue Diamond chalks, I've found this tool to be completely unnecessary. It will be essential if your chalk is not as adhesive as Blue Diamond.)
* Burnisher (I prefer a leather burnisher, but I carry an abrasive burnishing pad as well. Abrasive burnishers are usually a big no-no for the shaft - over time, you will regret using abrasives when your shaft begins to waste away - unless you have the money to do that, stick to leather burnishers, they are just as good, if not better, and seal the pores up well.)
* Microfiber Cloth (I usually wipe my cue down before and after use to remove any dust and debris deposits and preserve the pristine condition of the cue. Over time though, your shaft will age and that new-shaft look will disappear. Look at it as a prize. All your hard work is in there.)
* Cotton Towel (This is my dry towel. After wiping with a damp microfiber, I need to dry my cue, the cotton does a good job. I burnish the shaft moments after to seal back the swollen pores and get my shaft back into smooth shape for play. Also helps for wiping chalk dust off your hands.)
* Cue Holder (Worth wile to carry a cue holder with you where you go so you have somewhere to rest your cues safely without worry. It has come in so handy and is "Cue-Essential" to the case.)
* Chalk, chalk and more chalk (I normally carry around 4-5 cubes of chalk because I know anything can happen to your chalk. If you lose one, you still have another. Respect to your fellow players too, if they lost one or don't have one, you have one to offer them. Chalk is like money, without chalk, your game is useless.)
* Hand Talc (I have a small bottle of Johnson's Baby Powder with me - it's fragrant and still talc, so it does the job. I don't frequently use it, I don't like it getting on my shaft, in fact, I hardly every use it. But it's there should I need it. There are times when I wet my hands, or grab the wet microfiber I cleaned my cue with and my hand is too wet for the shaft to slide on cleanly - talc is the quick fix to drying up your hand on the spot.
* Magic Rack (I'm not promoting this or anything, nor am I advertising this. I'm just saying that the magic rack is nice to carry around in case you arrive before a table with no rack. Usually the case when I'm at my buddy's house - he broke his rack and neglected to buy one for so long, we had to rack up by hand. Comes in handy.) I will re-post this if the Magic Rack part is against forum rules and will be omitted from the re-post. I respect forum rules first.
Leave the heavy-duty tip tools, cleaning equipment and maintenance hardware in the repair case you brought with you - they will be cumbersome.
However, if you are using a soft tip or a super soft tip, you might want to bring a mushroom grazer and a cut rite around with you. There will be times when you play so long your tip will mushroom a little bit and you'll be searching for those two tools. If you're using medium to hard tips, just leave them in the repair case.
Some people carry around two playing cues - nothing wrong with that - I prefer one cue. It's good in a way that you find one cue to vest all your playing skill into, but if i'm going overseas with my cue case, or somewhere I know I won't be able to run home and get another cue, i'll bring two of my favorite playing cues (usually cues whose joints are threaded the same - giving me additional shafts that can be used on either cue, more versatile that way) just in case luck runs out on me with one cue (i'm superstitious like that). Totally nothing wrong with bringing more than one.