Lots and lots, but what's built into your DAW will take you quite far - that's what I generally use for EQ and compression.
There's a lot of free stuff out there and hard to filter through all of it to get to the good stuff. So here's a shorter list of non-DAW free stuff I keep coming back to:
RS-MET Toolchain for Engineers Filter which I basically just use for highpass filtering
AXP Flextron for guitar amp sim
Shattered Glass Audio Ace for low-gain guitar amp sim
Ignite Amps SHB-1 bass amp sim and NadIR cab sim
Samplicity's IRs of a Bricasti hardware reverb
Plogue sforzando sampler
Limiter6 for mastering
TDS Ferric tape saturation emulation
Non-free stuff I use a lot:
Eventide Ultrachannel though just for vocals
Pianoteq though there are nice free pianos out there and I mostly use it for guide tracks and transcribing songs, not much piano in final mixes
Levels for checking peak and LUFS but, again, free meters are good
Acon Digital Acoustica's denoise, declick and spectral editing tools for cleanup
Drum, bowed string etc. samples are also an area where non-free stuff is a considerable upgrade over what's free but that's getting outside of the topic of plugins, and is a really deep rabbit hole. But just for fun: take a look at Majetone Dream Kit Zenith. A mad-science synthesizer made entirely from drum samples. But if you're just recording all "real" instruments all the time, you don't need to look into this area at all.
Fabfilter and Izotope are very good recommendations, too, for suites that will cover all the very useful "general" basics. One of those and some instrument-specific amp sims will cover a lot of ground.
