Joined: Jan 2009
Posts: 44,139
Likes: 6,365
From: New York, NY, and High Falls, NY, USA
Bikes: 1962 Rudge Sports, 1971 Raleigh Super Course, 1971 Raleigh Pro Track, 1974 Raleigh International, 1975 Viscount Fixie, 1982 McLean, 1996 Lemond (Ti), 2002 Burley Zydeco tandem
Fit and comfort are most important, so if you can be happier with different handlebar tape or grips or a saddle or a stem that makes the fit better, that's all worthwhile.
As others said, tires. They're not sexy, and they're not as well understood as the other components of the bike, but they're critical. Nice tires make a nice bike.
And that's about it. There are occasionally good reasons to upgrade. As some say, wheels can be a worthwhile upgrade.