My preference definitely goes to analogue, "classic vintage" technology, that provides deep, warm and lush sounds in opposition to digital, which is more accurate and precise, more versatile but sonically less interesting...at least to my taste.
About 18 years ago, I started with some multi-effects like the Ensoniq DP/4, Boss SE-50 and Lexicon Vortex. All very capable and decent machines, but these were quite soon to be replaced by dedicated analogue processors and pedals.
The effect I most often use in my music is delay, and more specifically tape delay. There's nothing like the organic, self oscillating feedback sound or the fading echoes of a tape delay for that "psychedelic" touch in a production.
The first machine I had (until last week) was a Roland RE-201 Space Echo tape delay/spring reverb
Followed by a modified Evans ES-5 Sound Creator, with Sound-on-Sound capability (which I also sold some time ago). This one was a real oddity and produced some amazing Lo-Fi sounds.
Then came this marvelous Fulltone Tube Tape Echo. Excellent dynamics and wonderfully rich tones. A bit pricey but worth every cent.