Mostly it depends on where and how far you commute, and road conditions (sandy, snow, salt etc etc).
At a minimum what I do is: Daily : check tire air pressure.
Weekly :
Check brake pad wear, tire wear, clean/wipe down entire bike
Monthly :
Check chain tension, chainring/cogs for wear, lube chain, adjust brakes, oil all pivot points on derailleurs, brakes etc.
Annually : complete tear down, inspection and reassembly with synthetic grease on all bearings.
bicycles.stackexchange.com/users/32/M. Converse
My bike service guys wrote a blog article along these lines.
You may find it useful.
The article recommends four principals for basic bike care.
These are Keep your tyres pumped If it lives outside, use it.
An unused bike exposed to the elements will fairly quickly rust & seize up Lubricate - little & often, less is more Check your cables and bring back tension where needed
bicycles.stackexchange.com/users/73/Kevin
Being a big guy (~400lbs), I do a lot of damage to my bikes, so I check things more often and most of the time there isn't a problem.
It's just better to double check.
So as a result, here is my paranoid check schedule:
When needed: Brake fine adjust (at the lever to maintain feel).
Chain lube.
Chain cleaning (if it has been wet out, this can be more often than below).
Clean disc brakes with rubbing alcohol.
Daily:
Tire pressure by feel ( squeeeeze
, it's like a hug for your tires!).
Brake feel (give it a good hard stab on my way out of the driveway).
Every 3 rides: Accurate tire pressure.
Weekly: Headset adjustment.
It's a quick check, takes all of 30 seconds if it isn't out of adjustment.
Visually check the brakes for any damage or maladjustment.
Monthly: Bottom bracket adjustment.
Chain clean.
Wheel bearing check.
Accessory tightness (is that rear rack still attached?).
Lube rear cog bearings with chain lube.
Every 3 months: Chain ring bolts.
Pedal bearings and make sure they're tight.
bicycles.stackexchange.com/users/50/Jack M.
Just to Add to the already good suggestions,If you bike at night, Weekly Check headlights/backlights and Replace batteries; especially if you have a older incandescent (ie Not LED)
light
bicycles.stackexchange.com/users/7417/Lyndon White
This depends greatly on the type of bicycle: a Dutch type commuter bike requires very little maintenance.
Simply checking tire pressure weekly/monthly and maybe lubricating the chain once a year will keep it in good conditions for years (with minimal repairs needed).
The reason is that very few sensitive parts are exposed to weather and outside conditions: completely covering chaincase, internal hub gear, hub dynamo, etc.
My feeling is that it does help a lot to store the bike inside or at least under a roof to better protect it from rusting.
bicycles.stackexchange.com/users/7161/Jaap Eldering
What are the periodic maintenance tasks (weekly, monthly, annual, every X miles) that anyone who relies on a bike for transportation (typically in urban/semi-urban environments) should be performing? Ideally stated in terms of miles travelled (where applicable).
Periodic Maintenance Task for Bike Commuters
bicycles.stackexchange.com
<maintenance><commuter>
bicycles.stackexchange.com/questions/89
bicycles.stackexchange.com/users/63/noah
 Mostly it depends on where and how far you commute, the road conditions (sandy, snow, salt etc etc) and the type of bike.  The following checks are nevertheless recommended: Check brake pad wear, tire wear, clean/wipe down entire bike, headset adjustment weekly, visually check the brakes for any damage or maladjustment.   clean the chain (if it has been wet out, this can be more often than below) and clean the disc brakes with rubbing alcohol.    The answer may vary depending on average ride duration, road conditions and bike model. It would be a good idea to adjust the brakes, apply lube and clean the chain and disc breaks only when necessary. However, it is recommended that you check the tire pressure and break feel daily, while it will suffice to check the tires and pads for wear, clean your bike, adjust your headset, and inspect the breaks for damages once a week. On a monthly basis you could inspect the chain tension, check the chain ring and cogs, adjust the brakes and the bottom bracket, lubricate, and oil, among other things. You could check your lights and cables, change batteries and chain ring bolts more periodically. This may also apply for lubrication. Finally, it is not necessary to tear down your bicycle for a full inspection more than once a year.
The answer may vary depending on average ride duration, road conditions and bike model. It would be a good idea to adjust the brakes, apply lube and clean the chain and disc breaks only when necessary. It is recommended that you check the tire pressure and break feel daily. It will suffice to check the tires and pads for wear, clean your bike, adjust your headset, and inspect the breaks for damages once a week. On a monthly basis you could inspect the chain tension, check the chain ring and cogs, adjust the brakes and the bottom bracket, lubricate, and oil, among other things. You could check your lights and cables, change batteries and chain ring bolts more periodically. This may also apply for lubrication.  It is not necessary to tear down your bicycle for a full inspection more than once a year.