Coin cell regulation required?
I am designing a small PCB which I want to power using a CR2032 coin cell. 


OK. You've got 3 V when new.


  The circuit will include a 555 timer, ...


Yellow warning lamp! As far as I remember the original 555 timers draw a large current at the instant of output change. Consider the use of the CMOS version.


  ... a 40xx TTL ...


40xx is CMOS not TTL. CMOS should work OK but check the datasheets for minimum working voltage. TTL works in a voltage range around 5 V.


  ... and a few small LED's. 


Two things to watch for:


Watch the ESR (equivelant series resistance) of your CR2032. The more current you pull the more the terminal voltage will drop.
Bearing the above in mind, you need enough voltage (at full load) to power the LED and whatever voltage drop is across the transistor switch.



  I chose both IC's with a minimum supply voltage of 2V to make it work with the coin cell.


Sounds good.


  What are the conventions with powering circuits with a coin cell? Do I need to use a (linear) power regulator for this or can the battery be hooked up straight away?


Hook it up directly. You won't over-volt and any kind of regulator will cost power.