In general, an hero with a flat damage boost to their attacks benefits from at least some +AS items. Determining your final dps is a factoring problem. If your two axis are Damage and Attack Rate, your dps is Damage * Attack rate. Champs with high damage benefit from increases to attack rate, while champs with high attack rate benefit from increases to damage.
If the default champ attacks 1 times a second for 1 damage, he does 1 dps.
If you can buy items that increase his Speed or his Damage by 500%, you can do the following:
A champ that attacks 5 times a second for 1 damage each does 5 damage a second.
A champ that attacks 1 times a second for 5 damage each does 5 damage a second.
But if you split that into two 250% bonuses
A champ that attacks 2.5 times a second for 2.5 damage does 6.25 damage a second.
When looking at an increease in dps you need to consider the % effect on total damage or on total attack speed. 50 damage when you have only 50 is an 100% increase. 50 attack speed when you have 200 is only a 25% increase.
Champs that have a high boost to damage for free (mundo, chogath, Yi, etc) can add significantly to attack speed before a damage item becomes more cost effective. The actual point can be figured out with some algebra on a per champ/build basis, but often an estimate will do just fine.
This is what I think Phreak means when he mentions diminishing returns. (Correect me if I'm wrong? Attack speed is additive, yes?) Really, each attack speed item adds the same amount of DPS, which is a smaller % of your overall dps with each item., You might add more overall DPS by increasing some other aspect of your champions attack.