Not many options for that in Western countries. Even if you managed to get a combat deployment in the military, your odds of dying are quite low, and that's about as good as it gets. Not to mention, who's the last war hero you can name who gave his life for his fellow soldiers, democracy and the American Dream? A hero's death is worth 15 minutes of fame and a free burial.
Most of the world is more lethal, though... you could simply move to almost anywhere in Sub Saharan Africa, or a lot of the Middle East (I hear Lybia's beautiful this time of year), or get a job running drugs in Central/South America so a rival cartel takes you out, or most of South East Asia so their government does it for you. (The Philipines is lovely, and someone's certain to kill you for dealing drugs there). Not heroic by most people's definitions, but you could always say you're doing charity work, and some (small portion) of folks think that risking death to sell products people want to the people willing to buy them at risk of death is heroic, even if those products are vilified, but delightful recreational chemicals.
If none of that appeals, you could always do human rights related things in parts of the world where such things frequently result in death. A friend of a friend went to North Korea to essentially spy for Amnesty International, and hasn't been heard from in several years, so it's pretty clear what happened to him. Being an anti-Putin journalist in Russia is highly fatal as well. For that matter, you could go campaign for gay rights in Saudi Arabia, democracy and anti-corruption in Venezuela or be a Christian missionary in Indonesia. You wouldn't be looking at a quick, clean death, but you'd probably be hailed as a hero in these parts if/when your death gets noticed.
Sadly, Western governments are just smarter about such things. No sense in making a martyr of someone when you can assassinate their character and throw them in prison for life instead, so you'd have to travel abroad.
If that all sounds a bit fantastical, that's because the idea is fantastical, for the most part. Wanting a meaningful, heroic death is pretty common, actually achieving it is damn near impossible. Better to live a good life and help your loved ones (who deserve it more than some random cause or folks you don't know) than go out in a blaze of glory that inevitably goes unappreciated and is quickly forgotten by ungrateful strangers.
