Why hardware?

• Universal Audio LA-2A: arguably the best end of chain vocal compressor ever. Made as a set-and-forget box, its as close to magic as I've ever heard. Tubes and huge transformers absolutely change the sound. Also try it on bass!
• Thermionic Culture "Culture Vulture" Super 15: this is the "best of" Thermionic tube distortion device. Can do anything from subtle harmonics to all out annihilation. Once you hear it, you'll want it everywhere
• Overstayer Modular Channel 8755DM: dual mic preamps followed by analog filters (hipass and lowpass), tone EQ, compressor, then multimode saturation and distortion to sculpt from anything to anything. Studios call this a magic box for a reason; it just works magic. 
• Neve 1073LB with 1073 EQ: an all time classic mic preamp with all the sound and subtle tone you've heard thousands of times. Try it as a line input too!
• Purple Action Compressor (1176 clone) as shown in the picture, I have 100% of male rapper vocals hit this on the way in. It brings a presense thats not possible with just a preamp. Then it goes through the LA-2A. 
• Shadow Hills Mono Gama Preamp: the only preamp of its kind with 3 transformer settings; nickel, discrete, and steel.
• API 550b EQ: surgical EQ that cannot sound bad, no matter how you tweak it.
• Kurzweil KSP8 multi effects unit with RSP Remote: This is one of the last all in one multi-effects devices. It features top of the line algorithms from the great Massachusetts brain trusts, reverbs and delays and rotarys and on and on, AND you can stack them and configure them as you want...until you run out of DSP!
• Roland DEP-5: This is Rolands first multi-effects device, including reverb (multi-alg), chorus, and delay, with knobs for fast editing.
• Lexicon PCM60 vintage Reverb: This rack unit contains the room and plate algs you already know from the Lexicon 224 with ez buttons.
• OTO BIM, BAM, BOUM, BISCUIT: This French boutique company brings you the "best of" in the BIM (12-bit digital delay), and BAM reverbs with the Lexicon/EMT, and even Alesis. The BOUM is an end of chain compressor with drive. The Biscuit is the 8-bit CMI Fairlight frontend, followed by an Oberheim SEM filter
• Eventide H3000 SE multi-effects: considered by most as a 'desert island' piece, the H3000 has all the pitch shifting, reverbs, delays and many more that forged the sound of the 1980's, and Brian Eno's favorite!
• DeltaLab DL-5 HarmoniComputer: this is one of the first digital pitch shifters, with a handy keyboard layout to shift live up or down an octave
• Eventide 2016 Reverb: all the algs from the original 2016, plus new enhanced versions as well. One of the best vocal reverbs ever. 
• Eventide Eclipse multi-effects which was Eventide's first "best of" machines that could do dual processing. Roughly  4x the power of the H3000
• Korg GR-1 Stereo Spring Reverb will boing just like you want it to, but in stereo!
• Korg SDD-1000 12-bit digital delay. Pre-cursor to the SDD-3000, this one has all the knobs you need, and there's two of them for stereo!
• Korg SDD-1200: This is a dual channel stereo digital 12-bit delay. Fun for chorus, flange, vibrato, phase, or just standard digital lofi delay. Hear here
• Peavey Valverb tube Spring Reverb. Tube drive on the front, boing on the back. 
• Tech 21 Sansamp PSA-1: the first rackmount tube amp simulator, but it's all analog! Vocals from Beastie Boys? Guitar DI? Reamp drum loops? 2 for stereo!
• Tech 21 RPM This is the overdrive section from the PSA, with added tone sculpting. Try it on your mix with 2 for stereo
• WMD Geiger Pro: the best destruction/lofi ever made, with a randomizer. Two for stereo mastering, if you're crazy like me!
• Teaching Machines Fuzzbillion: this is a hardware gain/drive device that allows billions of sounds with the click of some buttons. Each click reconfigures the path with new circuity to dial in exactly what you're looking for. 
• Sherman Filterbank 2: The ultimate original filter channel to blow up your sounds. Listen to me do it here
• Electro Harmonix Bi-filter dual mu-tron filter clone for your wah-dreams

Bottom line: in order to use hardware, you have to touch it. And touching the knobs, sliders, physical control gives you license to experiment. In this experimentation, you find things you might not have heard before. When you do this, you critically listen without emotion, and removal of this emotion gives you freedom to sculpt sound from a non-writers perspective. This helps make your sound better, in my opinion. 

Hitting tubes with a drum loop is fun; dialing in the sound with tubes is better. 

Compression works for a reason; it tames your dynamics and makes the quiet parts louder.

Equalization and filtering shapes your sounds like they weren't before. 

And of course, saturation and distortion give a cumulatively better result when combined with other tracks. But you should be careful not to overdo it!

Tape: I tried it as a final mix glue and found that it didn't improve my already distorted sound, it just added noise. This might not be the case for everyone, however. And tape emulator VST's sound incredible these days. It was a great experiment, though! 

Finally, you might find your magic chain while trying to master something yourself. Sculpting highs and lows and compressing just enough and adding a sparkle and sheen might help your final product but make sure you listen critically and make it sound good to you!