Eggspectations (Snowden & 108 - near 100) is good, especially the eggs.
Double-T Diner is good up by Enchanted Forest (near Centennial Lane & 40).
The various Bagel Bins (there's one in Clarksville, Columbia, and Ellicott City) are OK - decent bagels, but they've gotten expensive and the service is iffy - there aren't a lot of other bagel options in Columbia, so if you really want one, it's your only choice.
There's a Panera in Dobbin Center and the mall
I second Bagel Bins and Eggspectations.
If you want something different for a casual breakfast, try Coffee Oromia in Burtonsville. It's on Rte 198 just west of Rte 29. It's a cafe/coffee shop run by an Ethiopian family. Good coffee. Basic eggs or omelettes. But they also serve Ethiopian grits and sambusa, which were like small samosas. And they serve what they call beignets. My wife says they aren't like New Orleans beignets, but they were light and sugary pastry. Not greasy. Something different.
I love the Hickory Ridge Grill - but be warned - you have to be HUNGRY to eat here! Breakfast is only served breakfast on Sunday mornings (9-2 pm, I think), but they have huge omelets (4 egg!), great breakfast potatoes, and pleasant service. They serve a wide range of "mediterranean" food - but their Greek specialties are their best. If you are starving, an omelet with gyro meat, feta, and tomato is just out of this world. I like their breakfast sandwich too.
Hickory Ridge Grill
6420 Freetown Rd Ste 120, Columbia, MD 21044