Litter is a reality anywhere in the galaxy. Even in the enlightened age where one can recycle anything, one needs to have the opportunity to do so. When peeps use certain services - such as grabbing a bite to eat at the Dine-O-Mat, washing up at the Lavotron, or buying something for themselves down at the shops - this leaves a plethora of wrappers, paper towels, and general rubbish with nowhere to go. If they have nowhere else to put it, a peep will simply drop the litter to the ground.
This is all well and good on stations with sufficient Scuzzer staff, as these busy little droids will stop buy to clean up (as well as recycle) garbage. Unless you reprogram them to be little cleaning machines, they will only do this if they have absolutely nothing else to do. The best way to be rid of litter is to have well-placed Litter Bins dotted around your station, particularly around those locations where litter is common.
Scuzzers (as well as litter bins) can only hold so much junk before they are running over. Scuzzers will destroy the litter if they have nowhere to put it. The best bet is to build a recycler as quickly as possible. With a recycler in place, Scuzzers will empty litter bins (as well as themselves) for you, filling up the recycling plant. When the workers stop by for a shift, that undesirable garbage will quickly be turned back into energy.
For those station masters who have a laboratory at their disposal, litter is a positive boon. By studying litter, Turakken researchers can determine the best way to be rid of it, and eventually how to clean the entire station. This leads them to design the litter bin, the Lavotron, and eventually the recycler itself.
There is danger in permitting litter to accumulate on your station. First off, your station visitors don't enjoy being in such squalor, and so they will leave. There are also vermin living under the deck plating of any and all stations. Once their is litter to eat outside, they will pop their fuzzy heads up for a papery treat. They carry diseases that will infect your populace. It gives you a nice profit margin on your station's Sick Bay, but also degrades the overall happiness of your visitors. The worst thing that can happen is when litter is left out in the open when you have a Memau aboard. Once they have eaten five pieces of garbage, they will enter the infectious stage, and - well - you don't want that to happen...