Can I create a collection of original 19th century public domain poems without violating copyright laws?
While technically you could claim a copyright on your collection, you would not have any claim of copyright for any of the individual poems included in that collection. The problem would be in getting any publisher to allow you to actually publish the collection.
All of the major e-book publishers have very strict guidelines regarding the republishing of public domain works. Amazon's Kindle guidelines in particular expressly forbid the publishing of any public domain works as part of a collection. They specifically require that you differentiate your work from the original in one of the following ways:
It is important to note that this criteria pertains specifically to the republishing of a complete public domain work. If you are trying to publish a collection of works, for example poetry, then their guidelines will not permit you to do so. This is especially true if these poems are freely available on the Internet.
Also, you will want to make absolutely certain that the poems you want to include truly are in the public domain. It is rare that individual poems are registered for a copyright because it is easier for a publisher to copyright a collection or an anthology. If any of the poems you want to use in your collection were copyrighted as part of another collection or an anthology, then that copyright may have been passed along to heirs or other parties.
On top of that, it is not uncommon for poetry to be published in multiple forms. For example, a poem may have been published in two different collections, but the author may have chosen to retain the copyright on only one of those collections. Another possibility is that the rights to a poem were sold to a publisher to be included in an anthology. In this example, the original author might have granted ownership of the copyright to the publisher.
It's a lot easier to ascertain that a full novel is in the public domain because it is essentially a single title. However, with something like poetry or short stories that tend to appear in many types of publications, it is harder to verify that each individual title is truly in the public domain.
IANAL - not a lawyer
It is hard to answer your question, because though it seems very simple, it is probably not the question you wanted to ask.
Can you create a collection of works. Certainly, even if they are still under copyright, as long as it is for your own use, and not made public. If you want to publish that collection, even if only on your personnal web site, for free, you have to get permission from the copyright holder or to restrict yourself to works in the public domain.
You specify that you are interested in "19th century public domain poems". If it is public domain, you have nothing to worry about (skipping possibly moral rights in some countries). But then why specify "19th century", which is an irrelevant information ? I suspect, possibly wrongly, that you think that they should be public domain because they were written in the 19th century. That is a wrong assumption.
The assumption is probably true if the poems were first published in the USA; I am not sure, since the history of copyright law in the USA created a very messy situation. However, even if written in English, or authored by an american citizen, these works could have been published first in another country than the USA. Then this other country is considered as country of origin of the work (Berne Convention art. 5). In that case, the general rules of the Berne convention apply, even for works published before 1923, and it is essentially the current US copyright law that has to be taken into account. The duration of copyright is author's life + 70 years. This means that the early works of an author who died in 1960 at the age of 90 will not be in the public domain before 2031, even though they were published in the 19th century. (this is in agreement with the comment of user dmm, though I do not know where he got the 150 years figure, which makes no sense to me).
Note, furthermore that when the country of origin is not the USA, the work need not be registered with the U.S. Copyright Office for its copyright to be protected in the U.S.A. (unlike works of U.S. origin). But the protection remains minimal without registration (see articles 411 and 412 of US Copyright Law).
Hence, to know about the copyright situation, you have to investigate among other things were the work was initially published.
The fact that copyright ownership may have changed hands, through sale or heritage, is totally irrelevant, except for the fact that only the current holder of the copyright may give you permission, and he must be identified and contacted.
The fact that the poem may have been published in several anthologies or collections is irrelevant. The country of origin for the copyright results from the first publication (see country of origin issue above). That means however that you may have to ascertain where a particular piece was published first, which may not be obvious for a small piece that may have been published several times, as part of different collections.
It is often the case that copyright is transferred to the publisher when the work is published, but this is not always the case. It is purely a contractual matter.
Another point is that copyright is not a monolithic entity. It can be cut in pieces. For example the author may have tranferred copyright for printed publication to his publisher, while retaining digital copyright. This is implicitly the case in some (many?) countries as the publication contracts before 2000 did not generally include transfer of digital rights.
So if you intend to publish your collection, the kind of rights you have to clear, and the rights holders who can grant permission, are not necessarily the same, depending on how you want to publish. However, the duration of these rights is the same and depend only on the date of the author's demise.
Note that you do not have to depend on publishers. It is quite possible to publish books without them. Indeed, one may wonder whether there is any reason for their existence in the digital world.
Another point is whether you can claim some rights over your collection. Essentially, yes, if it can show originality or serious investment (laws vary ... which is a problem for Internet publication), which does not mean simply being different from other collections - a very subjective assessment. This gives you no right over individual works in the collection.
And of course there are even more complicated situations. Copyright is mostly an exercise in futile complexity and obfuscation, at the expense of authors and public.