In Seoul, President Obama told U.S. troops, their families, civilian Defense Department employees and Korean veterans at Yongsan Garrison, "this nation recognizes your sacrifice, and we are grateful for your service, too."
Obama said the United States' commitment to its military means taking care of veterans after they complete their service.
"It's why I asked for one of the largest increases in the VA (Veterans Administration) budget in the past 30 years," he said.
Vice President Joe Biden participated in a wreath-laying ceremony the Tomb of the Unknown Soldier in Arlington National Cemetery in Arlington, Va.
In cities across the United States, Veterans Day parades and cemetery ceremonies were conducted to honor the nation's military, various media reported.
In Germany, first lady Michelle Obama surprised U.S. troops at Ramstein Air Base's Officers Club as she served them dinners during a Veterans Day meal, Stars and Stripes reported.
The first lady spent time with service personnel during a refueling stopover as she returned to the United States from her visit to Asia with the president.
She said she wanted to say "thank you" to the troops and their families from "a very grateful nation."
"We have a lot of work to do, but you all are helping move this country forward in so many critical ways," she said.
The first lady also met with more than a dozen wounded service members at Landstuhl Regional Medical Center.
A blogger, an Air Force veteran, urged people to thank veterans for their service, "whether they served decades ago in World War II or last year in Iraq."
Elaine Wilson said letting veterans know they're appreciated also lets them know "their service and sacrifice never will be forgotten," the Defense Department posted on its Web site.
In an e-mail, President Obama encouraged all Americans "to take time to thank the veterans, service members and military families in your lives and recognize their extraordinary service to our country."
He closed his e-mail by saying, "To all of our men and women in uniform, our veterans and our military families: We honor your service, we are grateful for your sacrifice, and we will not let you down."