On a nice day, you can always count on a bustle of activity by the "main" entrance, by Grand Army Plaza, where these serpentine decorative planters stand guard. (You're supposed to touch a snake for good luck before you go into the park, according to custom.*)
All told I've probably spent several weeks of my life in Prospect Park. New Year's Eve fireworks; an Audobon Society "bat walk" (we saw three kinds of bats); concerts at the bandshell (Richard Thompson in the rain being the most memorable); hikes through the Ramble and around Condom Wrapper Grove; spotting rabbits on Lookout Hill; exploring the local Revolutionary War history; paddleboating; communing with the Camperdown Elm (here's Marianne Moore's poem about it, and here's a bit of history; see below for photos); sledding down a snowy hill on a shred of plastic garbage can cover; my list goes on.
The park was conceived way back in 1859, and James Stranahan, President of the Brooklyn Board of Park Commissioners at the time, is rightly regarded as the "Father of Prospect Park." He is honored with a statue at the entrance, and looks like a kindly old man. More information on Stranahan here, and just about everything you'd need to know about the park here. Below are some images from a visit in early Fall. Only a few trees here and there were starting to turn.
This unofficial trail runs along the park's eastern edge, parallel to Flatbush Avenue
One of the park's many arches
It's beautiful by the lake in late afternoon
Ducks dig it
The Boathouse is the park's most striking building
Here's that Camperdown Elm
and a peek inside it
Could Monet have done better?
On the base of the memorial to the Maryland 400, whose brave stand enabled Washington's army to escape to fight another day
Clearing dead trees on Lookout Hill, victims of recent violent weather
The Lake from above—you can almost imagine you're in the wilderness
A meeting of the minds
A taste of autumn
Finally, for the younger set: I don't know how you play on this, but it looks cool
*It's a custom I made up. Please participate, and help establish my immortality.