The short answer is: No. 4 Gate is a powerful strategy with a lot of flexibility. This is because, as a race, Protoss is really dependent on their Tier 1 units. Since Protoss Tier 1 tend to be fairly tough units and a cheap caster, they can get away with this.
By comparison Terran Strategies are usually based around one of three different openings:
Each of which has its advantages. In terms of flexibility the 1:1:1 build gives you access to a wide arsenal of Terran units, but lacks the the synergy of upgrades, and thus relies on unit composition to make up. Meanwhile, Mech has very little flexbility and relies on the strength of Siege Tanks supported by Thor/Hellion to deal with Air/Melee. By comparison the 3 Rax has nice flexibility. I think this is the closest thing you're going to find to a 4 Gate equivalent.
The standard 3 Rax opening is: 2 Techlabs + 1 Reactor and producing 2 Marauder/2 Marine. Some of the nice tweaks to this are: Including Ghosts (great against Muta/Toss), Mass Reapers (powerful vs early game Zerg, with a transition into pure Marauder), Supporting with Siege Tanks (deals with most ground strategies), and even drops via Medivacs (powerful harassment and nice synergy with Stim).
By comparison, Zerg doesn't really have a nice normal build like these, though Roach/Hydra play is still fairly standard. Some people will say this is because Zerg adapt very quickly (all their unit production is shared), where as other might suggest that Zerg tech VERY slowly, and thus are forced to depend on their Tier appropriate units while trying to tech up.
I hope this helps.