It is possible to use the modern web if you keep the number of tabs low and switch heavier sites like gmail to the html mode. An ad blocker is needed and Youtube is watchable if you use the h264ify extension so it uses the hardware decoder and avoids modern video compression codecs.
I could even run libreoffice with Portuguese orthographic and grammatical checkers. It is slow, you can't run other tasks simultaneously but it works.
Want to watch movies? If it is 1080p or smaller encoded with h264 it is totally doable. Even streaming in 720p is doable. You won't be able to easily watch netflix though.
So, yes a 2GB Pi 2 is good enough for light browsing, light text editing, listening to mp3, watching movies and compiling software from early 2000's.
Things you can't comfortably do with it:
- Meetings: encoding and decoding with any codec that is not supported by the hardware is just too slow to be usable.
- Video editing: same as above. Also not enough RAM.
- Compiling large code bases: libreoffice and mozilla will probably fail on anything with less than 8Gb RAM. I could compile OpenCV on it, but it took hours.
- Keep many tabs open: you can if the sites are wikipedia-like. Anything more complex and the system starts swapping. Magic Sysrq-f is your friend in such situations.
- Modern IDE's: no way. Try gnu-nano or emacs/vi. Want to develop GUI apps? Use Lazarus-ide. Anjuta+Glade probably work stably with recent Gtk+3.x versions.
- Games: at the time I used it, the driver didn't support desktop OpenGL. Emulators for old consoles ran great, emulation station ran great, it is possible to run Quake but that is it.