Umm, well, weapons are frequently recurring, typically the stronger ones. The Last Fencer made its first appearance in Tales of Eternia as Reid's second most powerful weapon, and moved on to become Zelos' most powerful in Symphonia, and then it became Yuri's second most powerful non-Fell Arm weapon. And the Unicorn Horn is a frequent weapon in the series. Although usually now it's used as a "Devil Arms" sorta weapon.
There's been a frequent theme of discrimination/some sort of rejection going on as well, starting with Phantasia, although it wasn't really touched upon there. The first time they really touched upon racism in a Tales game was Tales of Rebirth, which is probably the 'darkest' game in the series. Darkest meaning more serious than others in the series >.>
Oh yeah, and then there's also the Summon Spirits, starting back at Phantasia, and then to Eternia as Craymels, then Symphonia, back as Craymels. There were summons in Destiny 2, but they were purely for Spell Mystic Artes, and played no role in the story. There's also the frequently recurring Artes and Spells in the series; Fire Ball has been in every single Tales game except two of them. And the Arte Demon Fang, or Majinken in Japan, is existent in every Tales game but Destiny 2; it's replaced by what's now Azure Edge, which really makes no sense, seeing as though its characters in Japanese, Souhajin, literally translates to "Green Destruction Blade"... So far, only three heroes have it; Kyle from Destiny 2, Stan in Destiny remake, and Yuri. Repede has it in Vesperia as well, but under the name of "Demon Dog".
Really though, if you see it in a Tales game, chances are; it's going to be in most of the ones after. Back in Rebirth, more Gumis were established; there are Peach and Grape Gumis now, but they've only been in Japanese only titles so far. Destiny's remake even went so far as to put in a crapload more Gumis, the only one that really stands out being the "Dragon Gumi".
I can't really think of anything else right now (Tired), but I'll let you know about any of them if you're still interested xD For now, enjoy this giant wall of text that you should've already read by the time you read this xD If not, then shame on you for skimming >(