The first case should really be done with === to avoid any type coercions, but depending on the number of alternatives you need to check it can become O(N), however depending on your code most JS engines will be able to a simple pointer check for the comparison.
In the second case you use a RegExp, and while RegExps are very fast, they tend to be slower for simple equality decisions than more direct equality comparisons. Simple string comparisons like yours are likely to be a pointer compare in a modern JS engine, but if you use a regexp the regexp must read every character.
The third case is more tricky -- if you do have a lot of values to check it may be faster, especially if you cache the object rather than repeatedly recreating it as it will simply be a hash lookup -- the exact performance of the lookup depends on the engine though.
I suspect a switch statement would beat the object literal case though.
Out of curiosity I made a test (which you can see here), the fastest approach (in a webkit nightly at least) seems to be a switch statement, followed by if, followed by the object, with regexp's last.