Someone told me that it is better to not have long peyot if you are going to place them behind your ears. Has anyone heard a respectable posek say that? I think he said it in the name of Rav Ben Tzion Abba Shaul?
To answer your question: It's been said in the name of Reb Chaim Kanievsky that one should not hide one's Peyot behind one's ears, but he never says to cut them.
There are plenty well respected Rabbis who hide their Peyot behind their ears, and others who have trimmed Peyot .
Just to put this in context, let's go back to basics - using classic sources.
The Torah forbids one to cut the hair in the Peyot area too short.
Details are in Shulchan Aruch, Yoreh Deah, siman קפ"א
How long must Peyot be?
Obviously long enough to not be considered "too short", but keep in mind the opinions (printed on the page in Shulchan Aruch) that say in the name of the Ari z"l that Peyot shouldn't grow into the beard area - and the Ari z"l used to trim his Peyot regularly.
None of the classic Poskim (until the 20th century) discuss what to do with long Peyot - and it would be interesting to see what the opinions mentioned in the various answers use as their primary sources for not hiding them behind the ears.
Regarding "embarrassed that they're performing a mitzvah":
Surely this would depend on time and location. In Bnei Brak it may seem that you are embarrassed, if you don't flaunt your Peyot. In Paris (for example, where Jews are regularly being beaten up) it's gutsy to even have Peyot behind your ears.
That said (about Bnei Brak), some of us are brought up on הצנע לכת and we don't flaunt our Mitzva observance.
I'm not sure about Rav Ben-Tzion Abba Shaul (I'd be very interested in hearing if anyone knows), but Rav Menashe Klein (Mishneh Halachos 7:121) quotes from R. Chaim Zvi Manheimer that people who grow their payos long and hide them behind their ears do look as if they're embarassed that they're performing a mitzvah, and that's a problem.
Personally, I would imagine that one is more likely to pull out hairs if they are longer, which may be an issue. I thought that the Debretziner Rav had a teshuvah about this but I can't find it at the moment.
However, I should point out that R. Binyamin Zilber (Az Nidberu 12:37) thinks that there's no problem, after all, where else should you put them that won't be annoying?