I believe in the power of wishes. I think your subconscious mind communicates with your conscious mind with wishes you are not aware of. I think wishing someone well also is a warm gesture. Here are some ways to wish well on others in Russian.

Wishes in Russian

Пожелания [pozhelaniya]

All the best!
Всего наилучшего! [vsevo nayluchshevo]

Have a nice trip!
Счастливого пути! [shchaslivovo puti]

Happy birthday to you
С днем рождения! [z dnom razhden’ya]

Happy Birthday in Russian

Happy Valentine day!
С днем святого Валентина! [ z dnom sv'atovo valentina]

Happy New Year!
С Новым Годом!  [s novym godam]

Merry Christmas!
С Рождеством!  [s razhdistvom]

Good Luck!
Удачи! [udachi]

Enjoy! (For meals…)
На здоровье! [na zdarov’ye!]

Bless you (when sneezing)
Будьте здоровы! [bud'te zdarovy] (means be healthy!)

Congratulations!
Поздравляю![pazdravlyayu]

I think the most know is happy birthday in Russian but also Merry Christmas in Russian.