When I was young, my older brother and I counted a bunch of pomegranates. Some totaled 607, 624, and other numbers in that area. Although none totaled exactly 613, in our series of counting the average came out to 613!
Thanks to msh, at the bottom of R. Zivotofsky's article I found that someone has an ongoing experiment regarding just this question and so far the average seeds in a pomegranate is ... you guessed it! 613!
See Ari Zivotofsky, "What’s the Truth about... Pomegranate Seeds?" for a general discussion about the claim that the fruits have 613 seeds each; his final footnote discusses the מציאות (facts on the ground).
Just to contribute a tiny bit of data (while agreeing with the other answers that the count varies):
Tonight I was dismantling a pomegranate while waiting for dinner to cook, and one thing led to another, and I found that this single data point had exactly 613 seeds. I only eat about one or two pomegranates a year, so I am unlikely to collect a statistically-meaningful sample in my lifetime. But there existed at least one, anyway. :-)
Parshablog cites a [somewhat dubious] study which claims that the average number of seeds in pomegranates worldwide is 613. He also states that Malbim is the source for the 613 claim.
Yes I have. No it's not literally true.
In light of Alexander Haubold's study, I now eat my words.
I heard that "filled with mitzvot as a pomegranate" is not a reference to a certain number, or even an abundance, but the "fullness".
אפילו ריקים שבכם מלאים מצוות כרימון is explained as being full like a pomegranate. When a pomegranate grows, its seeds fill it up leaving no space, as opposed to other fruit we know that have some extra space or inedible parts. The pomegranate fills all available space - so we wish to fill every ounce of ourselves with mitzvot, and even the "empty" among us are as full as that.
(Will edit upon finding the source. blndr)
In the new Artscroll biography of Rav Chaim Kanievsky zt"l - p.215 it notes how Rav Chaim was asked this question by Rav Zilberstein shlita.
Apparently Rav Chaim started thinking through the sources, and after a few seconds declared that it is not listed in Bavli. A few more seconds passed and he confirmed it was not in Yerushalmi. This repeated itself with statements that it was neither in the Midrash or Zohar.
Finally he asked for a Shir HaShirim with the commentary of the Malbim. It writes in Shir HaShirim 4:3:
כְּפֶ֤לַח הָֽרִמּוֹן֙ רַקָּתֵ֔ךְ
Your brow behind your veil, [Gleams] like a pomegranate split open
The Malbim writes there:
כפלח הרמון שהוא מלא תרי"ג גרעינין
Like a pomegranate split open - which is full of 613 seeds.
He then showed R' Zilberstein a Derashos Chasam Sofer Vol. 2, Shabbos HaGadol 5591 where it writes:
It is known that a pomegranate has 613 seeds, corresponding to the 613 mitzvos...I say that if the seeds represent the mitzvos, pomnegranate nectar - which is the primary part of the fruit - symbolises Torah, which is a fount of sweet pomegranate nectar. Thus, a pomegranate that is intact alludes to a scholar who engages in the study of Torah, which contains the 613 mitzvos, and who fulfills them.
It isn't true. In terms of the Malbim about 613 seeds in a pomegranate, see it inside, as well as a nice discussion by me and others, here: http://parsha.blogspot.com/2010/11/how-many-seeds-in-pomegranate.html
Of course not all pomegranates have 613 seeds; however, when I Googled - average number of of seeds in a pomegranate, the answer in the snippet block at the top of the search results page was 613. The source was: https://www.aquaphoenix.com/misc/pomegranate/