It's an old question, but an important one. Let's see if we can get a good, nuanced, ideally evidence-based answer.
So, old-school wisdom (certainly, how I was taught back in the day) says that serif text improves the readability of long passages of text. The eye passes over the text more easily, there is less "fatigue" on the eye, and reading speed is improved. As I was taught, this is the reason why book typesetters almost always use moderately florid serifs like Garamond. Sans-serifs, according to traditional wisdom, are better for legibility - the letters are simpler, less room for error - and so are better suited for short text, like road signs.
Within the last decade or so - certainly since reading on screens became commonplace - I've seen an increasingly common viewpoint that this is an outdated myth - that actually, serifs are faster for reading long text for no reason other than that we are historically accustomed to reading long passages of serif text, and that long passages of well typeset, well chosen sans can be just as good for readability and fast reading, as people become accustomed to it.
There's also a third viewpoint I'm aware of, which says that the second viewpoint is a myth that comes from the fact that serif fonts tend not to reduce well on pixel screens, making sans type the better (least worst) choice for long passages of on-screen text or poorly-printed reproductions, but serifs still the best for long passages of printed type. Hence the popularity of websites with sans body text and serif headers, and of printed materials with serif body text and sans headers. Essentially, it characterises the arguments for the second viewpoint as merely pointing out that good (well produced) sans type is better than bad serif type, and maintains that, for extended reading, all other things being equal, good serif type is better than good sans type.
And finally, there's a fourth viewpoint that it doesn't matter anyway - that there are no differences between serifs in general and sans in general that are not merely artefacts of the differences between the example fonts and typesetting used in any particular test or comparison. There's certainly a case to be made for this in the context of legibility, but I've not seen anything convincing on this for readability.
All other things being equal, do serifs on a typeface genuinely make lengthy body text easier (faster and less effortful) to read?
Readability (as defined by the speed of error-free reading) is something objective that can be, and has been, measured. This is a factual question. Can we give it a solid, rounded, nuanced factual answer?
A couple of asides relating to common arguments I've seen:
There's an old-fashioned justification for serifs based on the idea that the eye follows a line of text, and the serifs, by hinting at a cohesive horizontal, help the eye along its way. The first part of this is simply not true - the eye moves in numerous extremely fast jumps ('saccades') we are not consciously aware of, and the motion between jumps is too fast for any information to be taken in. It's 'Jump-focus-jump-focus-jump-focus', leading to one awareness of the area covered by the jumps. However, this doesn't completely nullify the gist of the argument. It's perfectly possible, for example, that serifs could help create implied cohesive horizontals in the blurred areas of vision outside the fovea which could help the reading process by guiding saccades and/or making word boundaries more distinct.
A point is sometimes made about serifs being a cultural artefact. That's undoubtedly true - but it's interesting to note that many scripts have optional equivalents to serifs which, like Roman serifs, mark significant protrusions and corners, and which in some cases have a history that can't be put down to simply following popular roman typefaces. For example, they're historically important in Chinese (and therefore also Japanese) writing, and interestingly, give a sense of direction that is both horizontal and vertical (makes sense as historically these have been written in a variety of directions). So, it's not grounds for dismissing serifs as just an artefact of one cultural heritage.
Finally, a related topic has been touched on over at the UX site, and second answer has many interesting references, but that question has no clear focus between readability and legibility, and so doesn't give a definitive answer on the readability front.