In addition to the mandated communal offerings, individual Jews were liable for, or permitted to bring, a variety of offerings of their own. How often did the average Israelite bring each type of offering in a year? Was this pretty routine, or unusual? (Sin-offerings and wellbeing-offerings seem like they could be pretty variable.)
The minimum of an average person had to go to the Bais Hamikdash for the 3 Regolim and that meant a Korban Olas Re'iya and a Chagiga. In addition, on Erev Pesach they had to bring a Korban Pesach (which was brought in groups as opposed to the individual). As far as how often a person would have to go to the Mikdash, even if a person is obligated to bring a Korbon s/he did not have to bring it straight away s/he had to bring it by the next of the 3 Regolim, if s/he did not then s/he would trangress a Mitzvas Asei. If s/he did not bring it by the end of 3 Regolim s/he would trangress a Mitzvas Lo Sa'saei as well. See Rosh Hashana 4a and rambam Hilchos Ma'asei Hakorbonos 14:13.
I don't think we have enough sources to be able to estimate how often the average person brought each type of sacrifice, save for one type - kinei yoldot (see further down). We can, however, estimate that the average person maybe went a few times in his or her lifetime to the Temple. This can be pretty safely said about the Second Temple, and is probably also true for most of the years that the Tabernacle in Shiloh was active. As for the other periods - I'm not sure.
Note: Most of this stuff was explained to me by one of my history professors. The kinei yoldot part is something I discovered via a shiur my grandfather z"l, formerly an economics professor and founder of the Economics and Halachah program at BIU, gave a few times on Shavuot.
The Second Temple:
Maccabees II, allegedly a summary of five books on the Maccabean Revolt written by one Jason of Cyrene, opens up with two letters written to the Jewish community in Egypt. Both letters were written a number of decades after the Revolt.1 In the letters, the Jews of Yerushalayim invite the Egyptian Jews to celebrate Chanukah with them. My guess is that if the vast majority of Jews came even just once or twice a year, there would have been no need to send a formal message inviting the Jews of Egypt to join in on the celebrations - decades after said events - because they would have been well aware of the festival already.
Philo mentions that he went up once to the Temple (On Providence, Fragment I):
"There is a city of Syria, on the sea shore, Ascalon by name: when I was there, at the time when I was on my journey towards the temple of my native land for the purpose of offering up prayers and sacrifices therein..."
Scholars generally agree that this means that Philo only came once (and some believe twice) to the Temple (being that he says "my journey" rather than "a journey" or "one of my journeys") - and Philo lived in Alexandria, Egypt, and was very wealthy and an important figure in the Alexandrian community - yet he was only able to come once or twice in his lifetime. What should we gather about people who lived farther away and/or were poorer?
There are also some Chazalic sources:
"...The incident in question was as follows: When nazirites were ascending from the exile to sacrifice their offerings, and they found the Temple destroyed, Naḥum the Mede said to them: If you had known that the Temple would be destroyed, would you have taken a vow of naziriteship? They said to him: Certainly not, as there is no remedy for a naziriteship in this case. And Naḥum the Mede dissolved the vow for them. And when the matter came before the Rabbis, they said: His ruling is incorrect. Rather, whoever took a vow of naziriteship before the Temple was destroyed, like these nazirites from the exile, he is a nazirite, as he committed no error at the time of his vow, and one cannot dissolve vows based a new situation. However, one who stated his vow after the Temple was destroyed is not a nazirite, as he vowed based on an erroneous assumption."
The mishna records an event in which a group of nazirites came to give their due sacrifices after the destruction of the Temple. Now, remember that the Great Revolt had been going on for 3 or 4 years before the destruction (depending on when one dates the destruction) and continued on in other parts of Judea for another 3-5 years (again, depending on different views), making entry into Eretz Yisrael in general and Yerushalayim in particular extremely difficult - yet these nazirites were apparently completely clueless about all of this!
In more aggadic fashion, the gemara in Yerushalmi Brachot 17 says:
"ודא מסייעא להו דמר ר' יודן בריה דר' אייבו עובדא הוה בחד יהודאי דהוה קאים רדי געת תורתיה קומוי עבר חד ערביי ושמע קלה א"ל בר יודאי בר יודאי שרי תורך ושרי קנקנך דהא חריב בית מוקדשא געת זמן תניינות א"ל בר יודאי בר יודאי קטור תוריך וקטור קנקניך דהא יליד מלכא משיחא א"ל מה שמיה מנחם א"ל ומה שמיה דאבוי א"ל חזקיה א"ל מן הן הוא א"ל מן בירת מלכא דבית לחם יהודה..."
Translation: "...And something that will assist in proving this interpretation, as what Rabbi Yudan, son of Rabbi Aibo recounted: Once there was a Jew who was plowing his field when his two oxen began to bleat. An Arab passed by and heard the sound. He said to him: "Jew son of Jew, untie your oxen and untie your pitcher for your Temple has been destroyed." And the oxen proceeded to bleat again. He said to him: "Jew son of Jew, tie your oxen and tie your pitcher for the King Mashiach has been born." Said [the Jew] to him: "What is his name?" "Menachem." Said he to him: "And what is his father's name?" Said he to him: "Chizkiyah." Said he to him: "Where is he from?" Said he to him: "From the royal city of Beit Lechem of Yehudah."..."
Though aggadic, we might see here an echo of the situation in the diaspora, in which the average Arab (then a more nomadic people than they are nowadays) was more knowledgeable than the average Jew on the happenings in Eretz Yisrael.
Finally, l'havdil, the NT describes Jesus and his disciples coming to Yerushalayim:
"As Jesus was leaving the temple, one of his disciples said to him, “Look, Teacher! What massive stones! What magnificent buildings!”"
We see from here that these men from the nearby Galilee, in their twenties and thirties, had never been to Yerushalayim before and were astounded by its size and grandeur.
In short, it seems that the average person hardly ever came to the Temple in his lifetime. Certainly, there are other sources that attest to the numbers that the city drew during the Regalim - but presumably, there was constant change in who came (i.e., same numbers, different people) - because it was very difficult to come every time.
One exception - kinei yoldot (nests of women after childbirth):
"With regard to a woman who has in her case uncertainty concerning five births, and likewise a woman with regard to whom there is uncertainty concerning five irregular discharges of blood from the uterus [ziva], she brings one offering, and then she may partake of the meat of offerings. And the remaining offerings are not an obligation for her. If she experienced five definite discharges of a zava or five definite births, she brings one offering, and then she may partake of the meat of offerings. And the remaining offerings are an obligation for her..."
According to the mishna - and as explained by my grandfather - it was customary for women during the Second Temple Era to bring childbirth or zava sacrifices only after several births or discharges took place - evidently waiting years before coming up to the Temple. It's possible that the mishna is referring to the average: On average, women came after five births or five discharges.
The Tabernacle in Shiloh:
Famously, in the story of the concubine of Givah, the survivors of the Tribe of Binyamin had to receive directions to know how to reach the Tabernacle in Shiloh (Shoftim 21:19-20):
"Then they said, Behold, there is a yearly feast of the Lord in Shilo which is on the north side of Bet-el, on the east side of the highway that goes up from Bet-el to Shekhem, and on the south of Levona. Therefore they commanded the children of Binyamin, saying, Go and lie in wait in the vineyards..."
Evidently people hardly came up to the Tabernacle, and this story, according to most views, took place pretty early in the Era of the Judges. A midrash further expounds on this, but also explains how the situation was remedied during the last years of the Shiloh Era (Tannah Devei Eliyahu Rabbah 8):
"אלקנה היה עולה לשילה ארבעה פעמים בשנה שלשה מן התורה ואחת שקיבל עליו הוא בנדבה...עלה אלקנה ואשתו ובניו ובני ביתו ואחיו ואחיותיו וכל קרוביו היו עולין עמו...וכשעולים עמו בדרך היו לנין ברחובה של עיר והיו מתקבצין האנשים לבד והנשים לבד שכן האיש היה מדבר עם האיש והאשה עם האשה וגדול עם הקטן והיתה המדינה מרגשת והיו שואלים להן להיכן תלכו ואומרים להם לבית האלקים שבשילה שמשם תצא תורה ומעשים טובים ואתם למה לא תבואו עמנו ונלך ביחד מיד עיניהם משגרות דמעות ואומרים להם נעלה עמכם וכן אמר להם עוד הפעם עד שעלו עמו לשנה הבאה חמשה בתים ולשנה האחרת עלו עמו עשרה בתים ולשנה האחרת הרגישו כולם לעלות והיו עולין עמו כמו ששים בתים ובדרך שהיה עולה שנה זו אינו עולה לשנה האחרת עד שהיו כל ישראל עולין והיה אלקנה מכריע את כל ישראל לכף זכות וחינך אותם במצות וזכו רבים על ידו..."
Translation: "Elkanah would go up to Shiloh four times a year: Three times from the Torah and once more that he took upon himself charitably...Elkanah went up with his wife and sons and his household and borthers and sisters and all of his relative went up with him...and when they went up with him on the road, they would sleep in the middle of the city and people would gather - the men by themselves and the women by themselves, for man would speak with man and woman with woman and an elder with a youth and the country would take notice and they would ask them: "To where are you going?" And they replied: "We are going to the House of the LORD in Shiloh for from there the Torah and good deeds shall come out. And you, why shouldn't you come with us and we shall go together?" Immediately, their eyes would fill with tears and they would say to them: "We shall come up with you!" And so he said to them once again, until they came up with him. By the next year, five houses came [with him] and the next year - ten houses, and the next year, everyone felt the need to come up, and some sixty houses would come with him, and in the road that he went up one year he did not go the next, until all of Yisrael would go up and Elkanah brought Yisrael to be judged favorably and he educated them in mitzvot and everyone merited by him..."
We see that for most of the time that the Tabernacle was in Shiloh, hardly anyone went up there, until Elkanah fixed this.
Interestingly, it is Elkanah's wife Chanah who, like the women after childbirth in the Second Temple Era, puts off the time of her coming to the Tabernacle after giving birth to Shmuel for a few years (Shmuel 1:1:21-24):
"And when the man Elkanah and all his household were going up to offer to the LORD the annual sacrifice and his votive sacrifice, Hannah did not go up. She said to her husband, “When the child is weaned, I will bring him. For when he has appeared before the LORD, he must remain there for good.” Her husband Elkanah said to her, “Do as you think best. Stay home until you have weaned him. May the LORD fulfill His word.” So the woman stayed home and nursed her son until she weaned him. When she had weaned him, she took him up with her, along with three bulls, one ephah of flour, and a jar of wine. And though the boy was still very young, she brought him to the House of the LORD at Shiloh."
So we find that even in ancient times, it was not considered problematic for a woman to put off bringing the childbirth sacrifice.
1 See Daniel Schwartz's commentary on the letters in his edition of the book for an explanation on the dating system used by the authors of the letters.