Well HGSS all up to Call of Legends are now rotated so apart from reprints, you probably won't want anything from there.
Off the top of my head there's:
Professor Juniper (BW Base, Dark Explorers)
Cheren (Emerging Powers, Dark Explorers)
N (Noble Victories, Dark Explorers)
Bianca (Emerging Powers)
Level Ball (Next Destinies)
Ultra Ball (Dark Explorers)
Pokémon Communication (HGSS Base, BW Base)
Random Receiver (Dark Explorers)
Pokémon Catcher (Emerging Powers, Dark Explorers)
Switch (HGSS Base, BW Base)
Super Rod (Noble Victoires)
You'll find almost all of those in pretty much every deck.
Here are a few others that aren't played in every deck, but can be played in a lot:
Heavy Ball (Next Destinies)
Max Potion (Emerging Powers)
Dark Patch (Dark Explorers)
Rare Candy (HGSS: Unleashed, Dark Explorers)
Eviolite (Noble Victories)
Tool Scrapper (Dragons Exalted)
Super Scoop Up (BW Base)
Energy Switch (BW Base)
Potion (BW Base)
Plus Power (BW Base)
Crushing Hammer (Emerging Powers)
Enhanced Hammer (Dark Explorers)
Skyarrow Bridge (Next Destinies)
Dark Claw (Dark Explorers)
As for the Pokémon, here are some listed below. Some listed might not be played in every deck but are seen in very common and extremely effective competitive decks.
Mewtwo EX (Next Destinies, Tin Promo)
Terrakion (Noble Victories)
Darkrai EX (Dark Explorers, Tin promo)
Rayquaza EX (Dragons Exalted, Tin promo)
Eelektrik (Noble Victories)
Hydreigon (Dragons Exalted)
Sableye (Dark Explorers)
Emolga (Dragons Exalted)
Garchomp (Dragons Exalted)
Altaria (Dragons Exalted)
Zekrom (BW Base, Tin Promo, Nest Destinies, Theme Deck, Box Promo)
Edit: Forgot the Energies >_<
Double Colorless Energy (HGSS Base, Next Destinies)
Prism Energy (Next Destinies)
Blend Energy (Dragons Exalted)
About Blend Energy, there are two different types of it. One that supplies Lightning, Water, Metal and Fighting. The other supplies Dark, Grass, Psychic and Fire. Both types are used so don't worry about deciding which ones to get, if you are getting any.
Also, just in case you didn't know, you can use cards in tournaments that have been reprinted. For example, Double Colorless Energy was reprinted in Next Destinies, which is legal. Because of this, I can use my Base Set 'DCE's in tournaments because that same card it legal. This can also apply to thing like Rare Candy from older sets.