When we look at the Spartans purely from a military vantage, we have to look at their won-lost record in order to find out whether history's image of them is veracious or not. I won't really run down the entire list of battles they ever fought, but of the ones we know, there were some wins and some losses. The truth is that most of the losses they experienced were on sea, and though they are undeniable, they are also pretty irrelevant to a culture that trained every minute of their lives for land warfare and never a solitary moment for the naval element. They infamously lost on sea at Arginusai and earlier at Pylos against the superior Athenian navy, but it is telling that Athens only once in the 30 year conflict we know as the Peloponnesian War offered a pitched land battle to Sparta and her allies. This was an unequivocal defeat for the Athenians.
The list of land battles for Sparta is ironically small. Or at least seemingly ironic since they were a land power bred for the phalanx since birth. But the reality is that Sparta was loathe to fight. In the first place, she did not like to risk the men she had so meticulously bred, and secondarily she simply was not imperial. In fact, the one time she became so (in inheriting Athens' empire post-war), her demise followed an immediate 30 years later. Sparta was not bred for conquest or the maintenance of a large kingdom (perhaps a confederacy, yes, as she had in the Peloponnesian League, but the very infastructure of Sparta was insular and only built to function within their own boundaries under very particular circumstances in which she could maintain that societal infrastructure). Sparta as we know it could only exist from within and, thus, she stopped at nothing to stay within.
As for the battles we do have, however, there are surprisingly as many defeats (even if only in technicality) as victories, so far as we know. They lost at Sphacteria (dubious circumstances but a loss nonetheless) in 425 BC, they lost in demoralizing fashion against Tegea around 550, and they of course lost in technicality at Thermopylai in 480. At Nemea they crushed Athens in 418, Persia in 479 at Plataia, and it seems that they also vanquised the Tegeans around 470. In this post I'm not going into intricacies of the battles, simply the record itself. And that record is two things: mediocre but more importantly, almost nonexistent for a four hundred year history. It's because of the reasons listed above as well as, in my educated opinion, that none wished to offer battle to the most feared warriors in Greece that the list of battles (certainly land battles) is so short.
There are also the issues that we have no inside sources from Sparta to help us uncover their martial record, and also that the source material before the Persian Wars in 490/80 is scant in comparison to that of Classical Greece (480 and beyond). Herodotus was recounting stories from before his own time, and he lived in the late fifth century BC. That means that not only could much of his information on the great war with Persia be dubious, but the material of a hundred, two hundred and more years prior about which he writes is in even more question. I'm not here to examine the veracity of the Father of History, just to make the point that it's hard to fully excavate Sparta's martial record from a time when largely history was left unrecorded. It is certain that the archaeological record may hold more clues to unravel this enigma, but I won't sit here and tell you that I know much of it. My knowledge lies in the primary sources of Herodotus, Thucydides, Xenophon, Plutarch and Pausanias and as far as they are concerned, I can state with absolute confidence the information I've offered.
When we look at Sparta as a military force and whole, their supremacy in the phalanx is unquestioned, and for good reason, but it is true that they owned their share of defeats. Even if only legitimately one or two, they were not unblemished. This truth does not detract from their martial greatness, it simply makes them human. None of us is perfect. Not then and not now. The greatest among us are flawed undeniably, and it is simply part of the human condition to be so. As I see the Spartans, and as the sources tell us, they came as close to perfecting their craft as possible and if you ask me (which maybe you aren't) they were as good as undefeated. But I cannot tell you they actually were. They lost and therefore they were not the machines history would have you believe. They were human. And that's okay.