Odin is many things - the father of Thor, ruler of Asgard. He's even the basis for "Wednesday". One thing he's not, however, is an Avenger - except for the time he protected Earth with the help of several primordial heroes. This begs the question - given Odin's history with Earth (or Midgard as it is known in Norse mythology), why doesn't he help Earth Mightiest Heroes more often?
Marvel Legacy #1 saw the first appearance of the Avengers of 1,000,000 B.C. The team consisted of Odin along with the Phoenix, the sorcerer Agamatto, the first Black Panther and Iron Fist, the Starbrand, and Ghost Rider - the later riding a flaming wooly mammoth. The team convened in order to do battle with a Celestial. Given young Odin's alliance with a group of Earth-bound heroes in the planet's pre-history, why didn't the All-Father team up with the team's successors, the Avengers?
Of course, historically, Odin isn't a big fan of Midgard. He finds his son Thor's preoccupation with the home of the humans to be aggravating, to say the least. After all, Midgard is but one of the nine realms that Odin presides over. He's also intent on grooming his son to take over such duties (which Thor has, several times, including in the current Donny Cates run). Of course, Thor doesn't get much job training when he's off galavanting with the Avengers, so it's understandable Odin wouldn't want to encourage Thor's errant personality.
It's likely Odin also has more personal reasons for avoiding Midgard altogether. As a member of the prehistoric Avengers, Odin was in a relationship with the cosmic entity the Phoenix. Even in 1,000,000 B.C., the Phoenix bears an uncanny resemblance to Jean Grey, suggesting the future X-Man might have been destined for the doomed cosmic role from the start. Odin might stay far from Earth to avoid memories of his ex. And since there hasn't been any indication (yet) of how either the team or the relationship ended, it's possible even the All-Father has relationship baggage he's not eager to revisit any time soon.
His past history also reveals new motivations for Odin discouraging his son from entanglements with mortals like Jane Foster. Instead of simply viewing Earth as a distraction, Odin could also view it as a place of heartache and eventual disappointment, and ultimately seeks to prevent his son from making the same mistake he made. While the likes of Jane Foster and the Avengers have earned the All-Father's respect time and time again, Odin knows they are mortal, and even his relationship with the immortal Phoenix Force proved ultimately fleeting.
Of course, this could all change in the near future. Odin has stepped down as ruler of Asgard, with Thor taking his place. This isn't the first time Thor has taken the role, but it is one of the only times when Odin himself wasn't killed or otherwise trapped. One has to wonder - what is he going to do with all his free time? Presumably, Odin will remain to advise his son from time to time, but it's also possible he could adopt a more hands-on attitude towards Midgard. After all, with so much of the prehistoric Avengers' past shrouded in mystery, his retirement provides the perfect opportunity for the All-Father to revisit his past. So while Odin doesn't regularly assist the Avengers, that could all change very quickly - whether the Earth's Mightiest Heroes want the help or not.