Yes.  Diminishing returns and ceilings do exist.

Sources: SimulationCraft-Swtor wiki, Sithwarrior forums, Askajedi blog

Attack and Damage Types
There are four damage types: Kinetic, Energy, Internal, Elemental. The first two are mitigated by armor, the latter two are not.
There are also four attack types: Melee, Ranged, Force, Tech. Attack type and damage type have no correlation, you can have any combination of the two sets (though not all combination exist in game). The first two are subject to defense (avoidance) and shield (partial mitigation), the latter two are subject to resistance. Resistances (which are just avoidance for Force and Tech attacks) are present as a mechanic, but very very few effects in the game grant them, so they can essentially be ignored.
Thus you can very easily have an attack that bypasses armor yet can be dodged or shielded (an internal melee attack, for example), or an attack that bypasses defense and shield yet is armor mitigated (an energy force attack, for example)

The Two-Roll System
SW:ToR uses a two-roll system to determine attacks. The first roll determines hit or miss (or dodge/parry/resist, which are effectively just different names for miss).
The second roll determines of a successful attack crit, was shielded, or was a normal hit. In the event that crit % + shield % is greater than 100%, crit chance overrides shield chance.

Primary Stats
Max Health = BaseHealth + Endurance * 10

Strength/Willpower/Aim/Cunning Damage Bonus = (Strength or Willpower or Aim or Cunning) * 0.2

Force/Tech Power Damage Bonus = (Force or Tech Power) * 0.23

Power Damage Bonus = Power * 0.23

Willpower/Aim/Cunning Healing Bonus = (Willpower or Aim or Cunning) * 0.14

Force/Tech Power Healing Bonus = (Force or Tech Power) * 0.17

Power Healing Bonus = Power * 0.17

Secondary Stats
Crit Chance % = 5 + 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( PrimaryStat / max(Level,20) ) / 2.5 ) ) + 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( CritRating / max(Level,20) ) / 0.45 ) )
Crit chance can also include a bonus from a secondary stat. Have a look at your damage or healing bonus on the character screen, if it includes a bonus from a secondary stat it will also have a small crit bonus from that stat calculated as + 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( SecondaryStat / max(Level,20) ) / 2.5 ) )

Hard Cap = 70% (5% base + 5% raid buff + 30% from primary stat on gear + 30% from crit stat on gear)

Crit Size % = 50 + 50 * ( 1 - ( 1 - ( 0.01 / 0.5 ) )^( ( SurgeRating / max(Level,20) ) / 0.1 ) )

Hard Cap = 100% (50% base + 50% from surge stat on gear)

Activation Speed = CastingTime * ( 1 - ( %AlacrityFromSkillsAndBuffs / 100 ) - 0.3 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( AlacrityRating / max(Level,20) ) / 0.55 ) ) )
Alacrity does not affect instant cast spells or the rate at which DoT's and HoT's tick, but does improve all cast time spells and channeled spells.

No cap theorized

Armor Damage Reduction % = ArmorRating / ( ArmorRating + 200 * Level + 800 ) * 100
Caps at 75%, although this is not achievable with current gear and buffs

Defense Chance % = 5 + 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( DefenseRating / max(Level,20) ) / 0.55 ) )
Hard cap = 35% (5% base + 30% from gear)

Shield/Glance Chance % = BonusOnSheildGenerator + 50 * ( 1 - ( 1 - ( 0.01 / 0.5 ) )^( ( GlanceRating / max(Level,20) ) / 0.32 ) )
Hard cap from gear = 50%

Shield/Glance Absorption % = BonusOnShieldGenerator + 50 * ( 1 - ( 1 - ( 0.01 / 0.5 ) )^( ( AbsorbtionRating / max(Level,20) ) / 0.18 ) )
Hard cap from gear = 50%

Basic Accuracy % = 90 + 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( AccuracyRating / max(Level,20) ) / 0.55 ) )
Accuracy over 100% reduces the Defense of the target, currently theorized through practical tests at cap of 108% Only your free level 1 attack is Basic.
Hard cap = 120% (90% base + 30% from gear)

Basic Off-Hand Accuracy % = 57 + 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( AccuracyRating / max(Level,20) ) / 0.55 ) )
Off-hand attacks are rolled separately to main hand attacks
Hard cap = 87% (57% base + 30% from gear)

Special/Force/Tech Attack Accuracy % = 100 + 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( AccuracyRating / max(Level,20) ) / 0.55 ) )
Accuracy over 100% reduces the Defense of the target, currently theorized through practical tests at cap of 108%
Hard cap = 130% (100% base + 30% from gear)

Special/Force/Tech Off-Hand Accuracy % = 67 + 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( AccuracyRating / max(Level,20) ) / 0.55 ) )
Off-hand attacks are rolled separately to main hand attacks
Hard cap = 97% (67% base + 30% from gear)

PvP
PvP Damage Bonus % = 20 * ( 1 - ( 1 - ( 0.01 / 0.2 ) )^( ( Expertise / max(Level,20) ) / 0.72 ) )
Cap is 20% from gear

PvP Damage Reduction % = 20 * ( 1 - ( 1 - ( 0.01 / 0.2 ) )^( ( Expertise / max(Level,20) ) / 0.72 ) )
Cap is 20% from gear

PvP Trauma Ignore % = 20 * ( 1 - ( 1 - ( 0.01 / 0.2 ) )^( ( Expertise / max(Level,20) ) / 0.72 ) )
Trauma ignore overcomes the Trauma (-30% healing received) debuff that players get in PvP, so it effectively improves healing.
Cap is 20% from gear

Companions
Bonus Companion Health = Presence * 5

Bonus Companion Damage = Presence * 0.2

Bonus Companion Healing = Presence * 0.14

Diminishing Returns
Further investigation into the formula's result in a diminishing return curve, not a linear increase. The more of these stats you gain, the less they benefit, until they reach a limit of no benefit at infinity. Endurance, Strength, Willpower, Aim, Cunning, Power, TechPower, and ForcePower have no diminishing returns and can be acquired at high levels without consequence.



Edits:  fun with images