I've used all three so here's my $0.02.
I really want to vote for Doug Schmidt and respect all the work he's done, but to be honest I find ACE mildly buggy and hard to use. I think that library needs a reboot. It's hard to say this, but I'd shy away from ACE for now unless there is a compelling reason to use TAO, or you need a single code base to run C++ on both Unix variants and Windows. TAO is fabulous for a number of difficult problems, but the learning curve is intense, and there's a reason CORBA has a number of critics. I guess just do your homework before making a decision to use either.
If you are coding in C++, boost is in my mind a no-brainer. I use a number of the low level libraries and find them essential. A quick grep of my code reveals shared_ptr, program_options, regex, bind, serialization, foreach, property_tree, filesystem, tokenizer, various iterator extensions, alogrithm, and mem_fn. These are mostly low-level functionality that really ought to be in the compiler. Some boost libraries are very generic; it can be work to get them to do what you want, but it's worthwhile.
Poco is a collection of utility classes that provide functionality for some very concrete common tasks. I find the libraries are well-written and intuitive. I don't have to spend much time studying documentation or writing silly test programs. I'm currently using Logger, XML, Zip, and Net/SMTP. I started using Poco when libxml2 irritated me for the last time. There are other classes I could use but haven't tried, e.g. Data::MySQL (I'm happy with mysql++) and Net::HTTP (I'm happy with libCURL). I'll try out the rest of Poco eventually, but that's not a priority at this point.