We rent an apartment in a nice area. On Saturday morning, our kitchen sink would not drain. I called the leasing office before 11AM and was told that someone would be out to look at it. By 4PM, no one had come by. I went to the leasing office and the manager said that the maintenance guy "May or may not show up today." After waiting another hour, I called the after-hours number and was told that a clogged sink was not an emergency and he would only work weekends on emergencies. I want to call a plumber myself but I fear that the apartment complex will stick me with the bill. Am I to go the whole weekend without use of the sink and dishwasher (which uses the same drain)?

Is the drain PVC (plastic)?
Are there apartments above you?
Is there a disposal?
It's usually pretty easy to unclog a drain yourself, and unless people live above you causing the clog, it's the user's fault for allowing food to go down the drain to get stuck.
The trap under the sink isn't glued on. Just remove the coupling at each end and empty/clean it out in another sink.
If you have a disposal problem, answer back.

As for landlords who won't clear a drain on a weekend... I am a bit on the fence, leaning towards the landlord's side, who is probably paying double time, and dealing with reports according to priority by type and not when reported. But it depends on who caused the clog. Landlord-tenant law doesn't try to identify the fine details about what is an emergency or even what a timely repair is, except in matters of heat, which varies by state law and sometimes city law.

If you don't want to try and clean the trap on your own, I would try getting some drain cleaner or a do it yourself snake from a local hardware store. If you still can't clean it then yes you have to wait until Monday.

I agree with joy, this is not an emergency and if you call a plumber you will probably be stuck with the bill.