Did other scientists have similar ideas at the time, that would lead us to the same conclusions today, but Einstein always got the spotlight because he was famous, or would 2013's technology and science look different today if it weren't for Einstein?
I mean is it more like with Edison "inventing the lightbulb" (many others did at the same time, or would've done it soon anyway), or would things be fundamentally different today?
Yes, other scientists had similar idea at the time, but the papers Einstein wrote were groundbreaking all the same. Those papers made Einstein famous, so it's not as if others' contributions are overlooked because of his prior fame. The only rumored stain on his character is that he "stole" ideas from Poincare's and Pauli's prior papers, but people who make those claims don't really understand how the scientific publishing process works. Even Edison [edit: I meant Einstein, not Edison] stood on the shoulders of giants.
With special relativity I can't help feeling Einstein's real insight was to treat the implications of the mathematics as really true - and wonder whether Lorentz had already done this, but not thought it worth mentioning (us mathematicians tend to have a slightly different conception of reality from physicists).
Of course that's only the first and by no means the greatest of his ideas.
I think that's a fairly accurate summary. The Lorentz transformation predates relativity. Einstein's genius was taking it seriously.
People who get too attached to the idea that the he must have created the theory from whole cloth might be offended by that idea, but... honestly, that really was a stroke a genius. A lot of very smart people had the mathematics all but yelling at them that the model of rigidly separate space and time wasn't working, and when you dig back into it, it was "yelling" for decades. (For instance, Maxwell's equations, first published 1861, have a speed of light that is simply a constant, not a function based on the velocity of the observer or anything else like that. In hindsight, this is obviously a Big Clue.) It really was a stroke of genius that he put it together.
Had he not, I guarantee somebody else would have. It may have been years later, or possibly even a decade later, but probably not much more than that. Eventually evidence would have started stacking up and the conclusion would have become inevitable. Einstein did it off of not a lot of concrete evidence. But we certainly would not be living in a world in which nobody had ever come up with the idea or anything stupid like that.
If you want to dig through it, I find http://mathpages.com/rr/rrtoc.htm Reflections on Relativity to be a dense, but fantastic book on the topic. (Ooo, this is the first time I've ever clicked through that link and seen the physical book finally exists, after years of me wishing for it. Nice.) RoR even digs back and shows how the Greeks had paradoxes that demonstrated the impossibility of a rigidly separated space and time, and had we taken those paradoxes seriously much earlier, who knows what we might have done.
(I do find it intriguing how much math from that era can be framed in terms of taking the ancient paradoxes seriously, really really seriously, and not just as wordplay. One of the biggest moments in 20th-century math history, Godel's Incompleteness Theorem, can be viewed as "simply" taking the ancient Epimenides paradox seriously. http://en.wikipedia.org/wiki/Epimenides_paradox )
this is all true until you get to general relativity, which took Einstein some 10 years after special relativity to come up with.
general relativity is by far Einstein's most amazing idea/theory, and as far as i know it doesn't have any obvious inspirations. Feynman said as much. arguably if you cobble together special relativity + the idea of space and time as being one space + the equivalence principle, you might be able to come up with the idea for general relativity... but probably not.
Einstein was the first (and it really was a breakthrough) to realize the exact nature of spacetime. He reformulated the Lorentz transformation to show that the passage of time actually changes in different reference frames. (Edit: apparently the reformulation was done by Poincaré, but he still had the idea of aether.)
I mean is it more like with Edison "inventing the lightbulb" (many others did at the same time, or would've done it soon anyway), or would things be fundamentally different today?