Basic toolkit for bicycle maintenance
I would classify tools into two groups.  The ones you ride with, and the ones you keep at home.  There may be a bunch of overlap, but it is harder to work with a multi-purpose tool, so if you end up using one tool all the time, a purpose-specific tool may be worth the purchase.  

Tools to carry with you:


Tire levers.
Patch Kit.
Multi Tool.

There are a plethora of these.  I'd suggest visiting your LBS to find one you like.
Should have all of the hex wrenches you need for on the route fixes.

Leatherman (optional).

When you need it, you need it.  Until then, it's just dead weight.



Tools for at home:


Hex wrenches (optional if your Multi Tool has them already).

Bikes tend to use hex bolts all over the place, so a nice set of these can make your life easier.

Regular wrenches (optional based on the bike).

Axel nuts, pedals, and a few other odd bits might use these.
I believe everything on my bike is a 15mm wrench.  So maybe just need one?
Also may be included in your Multi Tool.

Chain lube.

I prefer T9 lube, but I know a lot of people who run straight 30w engine oil.
Yes, you need lube.  Otherwise your bike will end up sounding like a hamster wheel.

Chain Cleaner.

If you ride enough that you are posing this question, you will probably need one eventually.  Road grime sticks to chain lube and can grind away at the soft internal workings of your drive train.
They're also pretty cheap and really easy to use.



Other Tools:


Chain breaker.

This is useful if you need to replace or shorten your chain.  Until then, it isn't really needed.
May be included in your Multi Tool.

Bike stand.

Almost never necessary.  Nice, but not necessary.
Most of my bike work is done with the bike upside down on the carpet at home.

Cone wrenches.

Really nice if you know how to adjust your bearings.  I don't, so I take it to someone who does when they are out of adjustment.

Bottom bracket tool.

Most of the time your bottom bracket will not need maintenance, so it is easy to take it to your LBS.



That is everything I can think of right now.