A Quick Note
First of all, you should understand the importance of having a gym kit that is well stocked and ready to go at all times. The point here is that going to the gym is the most difficult aspect of working out - yes, you read that right; going to the gym is where most people fail. Once you're at the gym, there's a good chance that you are going to work out at least a bit and get some use out of it; but if you don't go at all then you'll accomplish nothing. As such, it is highly important to make sure that everything is working in your favour to make going as easy as possible - anything that makes it require more effort might just make you skip it. Having your kit prepared the night before and ready to grab will mean there's less conspiring against you to keep you indoors.
At the same time, for those partaking in sports this is a perfect way to help you stay calm and collected in the build up to your game. Having to rush around and prepare everything will only stress you out and will only take you more time - be ready to go and then you can relax and get into the right frame of mind for the competition.
Things to Pack
A Dry Towel: Make sure you have a dry towel. You should also take a plastic bag with you to put this in once it's wet so that it doesn't get everything else damp and covered in mildew. Each night when you get back from your sport or workout, just take the towel out and hang it up and then switch it for another one on standby (this way you can alternate between two towels).
Shower Gel and Deodorant: This is of course very important to make sure that you are not going to stink after your workout or game. A good idea would be to buy yourself a separate deodorant and a separate shower gel that you can keep permanently in your bag; this way you won't have to remember to keep them in the bag in the morning - they will always be ready to go (and you won't get into the shower in the evening only to have to run around the house naked to find your gym kit).
Protein Shake/Energy Drink: An energy drink is actually only necessary for very intense cardio that results in your sweating a lot and losing lots of blood sugar and electrolytes. If you are going for a long run or engaging in lengthy sports, then make sure that you take an isotonic sports drink. A protein shake meanwhile (or bar if that's easier to transport) can help you to recover after training and build muscle during the crucial 'anabolic window' that occurs after a workout.
Food: If you are likely to want food after a workout, then pack a lunch box and make sure to prepare this the night before too. Make sure this food is conducive to training or recovery. A water bottle also is a must.
Sports Clothes and Equipment: Whatever you need for your chosen sport or training regime must also be packed. If you train or play more than once a week, then make sure that you have lots of kits/joggers so that you can cycle through them quickly and avoid wearing the same set over and over. You also need to have two pairs of undergarments - one pair that you wear during your game/session and one for the rest of the day ahead.