One of the more amusing pastimes (well, for me anyway) when a saxophone client calls is to have a bit of a rummage through their case to see what's in it. I hasten to add that I don't do this on the sly, rather I do it with the client - usually because I've asked them what mouthpiece they're using, and because they can't remember the exact model number they then have to dig around in the case to find it. That's where I come in.

You might think that the larger a case is, the neater and less cluttered it ought to be - but it's fact of life that the more space you have, the more junk you'll find to put in it.
Thus, whilst the punter with a shaped fibreglass case may only have room for a mouthpiece and a box of reeds, you can be sure that they'll somehow cram in a microphone, a lead for same and half a photocopied fake-book. Similarly, the player with a larger case, perhaps of the vintage variety, will have all of the above plus a stand, a couple of spare mouthpieces, half a dozen reedcutters (none working, of course), a couple of bottle openers and pair of maracas.

Surely there comes a point where the size of the storage space in the case exceeds the potential volume of all the knick-knacks and accessories that the average working sax player is likely to accumulate? I'm afraid not, and I refer you to my opening sentence of the last paragraph.
It's also a strange quirk of fate that the larger the case, the more likely it is that you'll need some quite esoteric accessories. Take, for example, the baritone sax case.
A decent modern case, at least the one that originally came with the horn, is a hefty old beast, and being typically rectangular these days there are often a number of sizeable compartments to play with. You'd be surprised how quickly the compartments fill up - and here's a list of what I'd consider to be the absolute minimum you'd require:

For a start you'll need at least three mouthpieces (and they're by no means small affairs). A big ebonite job, perhaps an old Link, for the big band gigs; a hefty metal Lawton for the soul gigs - and one other piece, possibly a Runyon Quantum, that you bought in the (vain) hope that it could do the job of the other two pieces. You'll need a roll of tape of some kind to wrap around the crook cork on the grounds that the mouthpieces will have differing bore sizes, and none of them truly fit the crook cork anyway. Then you'll need some reeds. Bari reeds are huge, and a trip to the music shop results in your having more wood in your case than the average timberyard. If you're a cheapskate you'll keep them in the bulky boxes they came in - if you're flush you'll buy several plastic reedholders....and still keep the boxes the reeds and the reedholders came in.
You'll need at least two slings...one being of the harness type, the other a plain sling. You'll wear the harness type for the jazz gigs, where the emphasis is on playing the music. You'll need the plain sling for the other gigs - i.e. those where there's half a chance of a 'romantic liaison' - because your chances of pulling whilst wearing a harness are pretty much zero.

You'll also need a spare pair of trousers. At some point on a gig you're going to get careless with the top bow water key, and a casual flick of the key whilst the bass player takes a solo is going to dump about a quarter of a pint of gob down your slacks. The resulting water mark on your keks will complement the wearing of a harness a treat - and if you manage to pull on gig after that lot then it's very likely going to be something you'll regret in the morning. And for a very long time afterwards.

Some kind of telescopic stick is handy thing to have - an old car aerial, for example. This is to fish out fag packets, beer mats, dog-ends etc. that some witty punter thought amusing to chuck down your bell while you were having a swifty at the bar. The items inevitably sink into the pool of foul water that resides in the bottom bow, and no amount of shaking the horn will dislodge them (you'll just get more water on your keks)...hence the need for a stick thing to fish the rubbish out. If you're canny you'll have two such sticks - and you can get a couple of the trumpet players to compete on who can get the most gubbins out of your bari before the bandleader calls for the second set.

A battery operated lamp is essential. The bari chair is not a glamorous one, and unless you're good enough to be playing Carnegie Hall sized venues there's a fair to middling chance that you'll always be standing at the extreme edge of a stage. This is never lit - no lighting crew worth its salt would waste a spot on the stage fringes, and if you're lucky enough to have any light at all then it's extremely likely that the crew will have stashed all the spare gels on the lens...and you'll be bathed in a peculiar sort of light that actually makes the stage a little brighter when its switched off. Your battery lamp might not be powerful enough to enable you to see the music in front of you, but it should at least be bright enough to enable you to see what people are chucking down the bell of your bari.

Similarly it pays to have your own mic. Just like the lighting crew the sound guys won't waste their best mikes on the bari - and more often than not you'll end up with a mic that says 'Tandy' on it. If you're lucky.

Take a good book. On the average r&b/soul gig the solos will be hotly contested between the alto and tenor saxes, the trumpet and bone, and the guitarist. Even with a fair-minded frontsman you're always going to be waiting a while before the solos come around...and what often happens is that one of the others 'gets on a roll' and does a double chorus. By the time the nod gets round to you the frontsman will have wisely decided that whilst the punters enjoy a good solo, no-one wants to listen to a round of improvisation that goes on longer than a gatefold Yes album.
The smart thing to do is to have a quiet word with the frontsman beforehand - and on the basis that the bari player gets barely two solos in any gig you can arrange to do yours in the first two numbers...thus leaving you free to settle down to a spot of reading for the rest of the gig, safe in the knowledge that no-one will spring any surprise solos on you.

Finally, with all this stuff and gubbins stashed in the case, along with the bari itself, you're almost certain to do yourself an injury...so pop a truss in the case too..you're gonna thank me for it one day...

If there's any spare space left over you can reduce the overall weight of the whole ensemble by placing helium filled balloons in the remaining crevasses. This should result in a nett weight reduction of about half an ounce. The balloons can also be tied to your bari whilst you're on stage, which lends you a very festive look...as you sit there, in your wet trousers, reading a book by the light of a flickering bulb.