There are two aspects to the question. You asked about what parts would improve the riding experience with maintenance or replacement. You also could consider upgrading some items as they wear out.
Parts to maintain
Chances are that your chain and cassette were worn out. As your chain wears out, your shifting will get sloppier. If you change your chain before it wears out, you usually don't have to change the cassette as well. Chances are that your chain was worn out, and your cassette was worn with it. Anyway, when you replaced your chain and cassette, you have better shifting.
Keeping your chain clean makes it last longer and shift better. This article has some discussion on how do to so.
Your cables stretch over time, and dirt will get into the housing and make shifts sloppier as well. Very active cyclists who maintain their bikes well might still have the cables changed every 1-2 years. Chances are you will want to have them changed also.
The bearings in your hubs will also wear out over time. If you have cup and cone bearings, you should regrease them periodically, perhaps every year. If you have cartridge bearings, you can leave them until they start running roughly, then have a shop pull and replace the cartridges. You can do this yourself, but you'll need a bearing puller and press. Alternatively, you can gently remove the seal from a cartridge bearing, clean and re-grease the ball bearings inside, then replace the seal.
Your tires also wear out. With the amount of riding you say you have done, they may still be good. If your rear tire is squared off, you should probably change it. Otherwise, replacement is optional. You definitely don't want a worn out tire on the front, as that can affect your bike handling. I suspect that because the rubber wears away as you ride, worn tires can puncture more easily. I'm not sure there's empirical evidence of this.
Your question implies that you know you have to change your brake pads occasionally. For completeness, I'm adding that. You may also benefit from making sure your disc brake rotors are clean if the brakes start squealing. For rim brakes, I'm adding a link to suggested maintenance items here. As discussed, cleaning the pads and rims regularly is necessary and helps reduce wear. You want to check that your pads are contacting the rim correctly and that they're centered.
Partly related to rim brakes, you want to true the rims occaisonally. This is a bit harder to do yourself, as it requires a spoke wrench and preferably a truing stand. If your rims are out of true, they can rub the brake calipers, and if they are very badly out of true they will rub the frame. With disc brakes, if the rim is out of true, I think it's not as big a problem. I would still keep them adjusted on principle.
You didn't say what type of bike you have, but if it has a suspension fork, then many of them require maintenance to keep operating well.
Drop bar bikes have bar tape. It wears out over time. You should have the tape changed with the cables.
Parts to upgrade
I'd think about upgrading your tires as they wear out. Your stock tires may have wire beads, and you might get a better model kevlar-beaded tire. The kevlar beads will be lighter. Better tires usually have lower rolling resistance, so you expend less effort to get to your destination.
Stack Exchange normally frowns on product recommendations, but I'm going to link to the Continental Gatorskin as an example of a puncture-resistant and durable road bike tire. Something in this class of tire should be an upgrade over the stock tires that would come on a lower-end commuter bike.
If you are using rim brakes, then the stock pads on cheaper bikes may not be that high performing. You could replace the pads with a cartridge holder and a good pad that has better all-weather performance. I am thinking of something along the lines of the products made by Kool Stop. In my experience, good pads do stop quite a bit better. I have a pair of cheap Tektro mini-V brakes on my cyclocross bike. I put Kool Stop pads on the front one, and I have the cheap stock pads on the rear. There's a noticeable difference in braking power and consistency. The front is just fine. The rear feels a bit mushy when I brake.
I am new to disc brakes, so I'm not sure what upgrade options there are for pads. In case you're wondering: it's not possible to convert a rim brake frame to disc brakes. You could buy a disc fork and run a rear rim brake, but I question if this is worth the expense compared to just buying a new bike at that point.
In some cases, I think it might be worth upgrading the brakes themselves if the original brakes are poor and if upgrading the pads doesn't improve your braking enough. I'm just including this for completeness, since upgrading just the pads can be a significant difference. For rim brakes, if the calipers are flexy, then they won't provide as much braking force. For disc brakes, if you upgrade from cable actuated brakes to hydraulic brakes, you would need new shifters as well, which would make this a big expense. I'm not sure that sort of upgrade would be worth the effort. I'm thinking more of upgrading to a better cable actuated disc brake or to a better rim brake.
What lubricant you use on your chain can matter in terms of chain longevity. Thicker, oil-based lubricants can attract dust or dirt because they're sticky. Aesthetics aside, dirt that's sticking to your chain lubricant will then act as an abrasive paste, accelerating chain wear. A lot of dry lubricants contain relatively little actual lubricant; they're mostly a volatile (i.e. evaporates easily) carrier which is supposed to get the lubricant inside your chain before evaporating.
This article discusses chain lube selection from a performance standpoint (i.e. they consider friction as well as longevity; the former may not really be relevant to you as we're talking differences of 5 watts between the very worst lube and the very best). The article does recommend two particular chain lubricants or one particular wax. Waxing is much more involved than just lubricating your chain. I don't really want to get into which products to recommend, and you'll have to read for yourself.
Last, a minor point: some of the more premium bar tapes for drop bars are cushioned, which can take the edge off bumps in the road. This may be worth a thought when you get the tape changed.
