Oliver Knill's Interactive Dynamical Systems Lab (a great introduction to flat billiard problems and dynamical chains. )
Dan Archdeacon's Problems In Topological Graph Theory (hours of fun and hair loss)
Open Problems in Topological Graph Theory (Via Open Problem Garden) (OPG is fun as a whole, but this is my favourite page)
MIT OpenCourseWare (Mathematics) (I owe a bit of a debt to OCW for helping to get my mathematical ball rolling)
A Giant PDF filled with Open Problems in Various Sub-fields of Topology (authours: Jan van Mill and George M. Reed) (from 1990, so I'm guessing a few of the problems are no longer open [e.g.; on pg 434 you'll see the Poincare Conjecture is still listed as open even though Perelman famously proved the conjecture in 2006])
A List of Some Open Problems In Low-Dimensional Topology (More fun! More hair loss!)
Career (And Education) Advice From Terence Tao (I especially like "There's More to Mathematics than Rigour and Proofs" and "There's More to Mathematics than Grades and Exams and Methods". Prof. Tao is widely regarded as a giant in....well, any and every field of mathematics, and when you get a chance to get advice from someone of his stature, take it. His blog is fun in general.
ShareLaTeX (we all have our TeX editor of choice.)
NOTE (9/17/18): ShareLaTeX has merged with Overleaf. If you liked ShareLaTeX, you'll love Overleaf v2.. The LaTeX editor is exactly the same as ShareLaTeX, which I found to be ridiculously user friendly. I mean, srsly, if my barely-able-to-type booty can use it, then anyone can.
Prof. Richard E Brocherd's Algebraic Geometry Playlists (courses from Cal-Berkeley 2020 academic year. There's some glitches in the videos, but otherwise there's a lot of good stuff here. Follows from Hartshorne's book, but adds a lot of good insight and elucidation. I found the lectures to be very helpful in undertaking self-study of Hartshorne's book.)
Playlist 1: Varieties
Playlist 2: Schemes
Playlist 3: Extra Topics
Playlist 1: Varieties
Playlist 2: Schemes
Playlist 3: Extra Topics
Prof. Ben Webster's Fields Course on Symplectic Geometry (from The Fields Institute). 24 video playlist, with individual videos ranging from about 44 minutes to 2 hours. Most are about 90 minutes long, give or take. I haven't made it through the entire playlist yet, but the videos I've watched are of pretty good quality. Minimal glitches. Prof. Brocherd's course above was given in 2020, while this one is from 2021. I think the quality benefitted from the extra year of innovation in the technology. What with the pandemic and all.
Playlist
Playlist