I'm not a hard-core science fiction fan, so although Anderson has written enough SF to sink a ship, I can't make any recommendations.
But as for his fantasy, that's another story. Anderson has written some of my favorite fantasy of all time. You've probably heard of Three Hearts and Three Lions--some consider it his best in the fantasy genre, especially around these parts, due to its obvious influence on D&D (an iconic paladin, a green-skinned regenerating troll, etc.).
But for my money he's written better fantasy. If I were you, I'd start with The Broken Sword. In a field crowded with bloated, overwritten, 3 or 7 or 12 part series, Anderson in under 300 pages manages to spin a fantasic epic tale combining Norse mythology, inexorable tragic fate, faerie races vs. encroaching humanity, and Christianity vs. paganism. It's quick-moving, bloodthristy, and utterly enthralling.
Also amazing were Hrolf Kraki's Saga and War of the Gods. These are Nordic fantasy all the way, full of war, passion, betrayals, revenge, grim destiny, etc. You might find them hard to track down but they're so worth it.