Next to reverb, delay is one of my favorite effects. Being a child of the `60s I tend to prefer delays that have a bit of a tape-echo vibe rather than the pristine precision of `80s-style digital delays. In this article I'll briefly review the delay units I've owned over the past seven or eight years.
Korg used to make a stompbox called the 301dl. It runs on 4 AA batteries or a standard 9V adapter. The Korg is incredibly flexible for a stompbox echo, particularly given its size. There are four knobs controlling a total of eight settings via a mode toggle. Two presets are selectable from a stomp switch. There's no tap tempo. In addition to the usual echo functions, the 301 has a predelay adjustment, high and low cut tone controls, a knob that seemed to reduce the quality of the echoes (bit decimation?) and a ducking control. The last time I saw one of these it was going for around $100. If you're into pristine clean echoes and bypass you might not like this. It's a lot of fun, though. The only other stompbox echo with as much functionality is the new Eventide unit at $400.
Speaking of non-pristine delays, the new Boss RE-20 Space Echo emulator has a lot of personality. The RE-20 emulates the classic Roland RE-201 space echo, right down to the abysmal-sounding short-tank reverb unit. If you like the quirky sounds of tape echo, you'll love the RE-20. The warble, the distortion, the low-fi echoes... it's all in there. Everything, that is, except for the tape hiss. All that vintage-sounding goodness and tap-tempo, too.
The Akai Head Rush E2 (the blue one, not the older silver one) has four "heads". Each of those can be run to a separate amp if you like, or you can use the main output that mixes them all together. A control alters the "spacing" of the heads. There's a tape-delay emulation and a clean digital-delay setting. There's a very usable looper, too. You can switch among the three modes using the stomp switches. Yes, it has tap tempo.
The Electro-Harmonix Stereo Memory Man with Hazarai is a digital delay with lots of bells and whistles. It does modulated delays, digital delays, reverse delays and a looper. A single tone control changes the tone of the echoes, ranging from low-cut at one extreme to flat in the middle to high-cut at the other extreme. I don't particularly care for the way the SMMH's looper works (you hold down a stomp button to record), but it does loop the effected sound. There are some other unusual features that sets this unit apart, notably a kind of reverb that surrounds each echo repeat and the ability to set a definite number of repeats (these features don't apply to all modes). The SMMH has stereo ins and outs and tap-tempo.
The analog Deluxe Memory Man has a lovely tape-ish sound. It's great for trippy effects, but horrible for clean delays. It's probably best used with compressed or distorted guitar sounds, as the compander (the chip that gives those BBD chips a usable dynamic range) adds a noticeable thump to the note attack.
The Toadworks Redux is another unique unit having two "heads", one of which seems to be returned out-of-phase. This makes for some amazing textural effects. The noise floor is fairly high. No tap tempo.
If you can find one in good condition, Morley used to make an echo/chorus/vibrato pedal where the delay is controlled by the treadle. Again, something like this is great for psychedelic effects. I don't see many of these. They seem to go for close to $300. For that kind of money I'd go with a Boss RE-20 and an external expression pedal to control the delay time.
The Visual Sound H20 is a nice warm-sounding digital delay plus an independent chorus in one pedal. No tap tempo. Not true-bypass, but the buffer is excellent.
The Alesis Nanoverb is a 1/3-rack unit that has a nice delay plus reverbs, chorus and other FX. You have to use this in a low-Z loop. I used to have a monster pedalboard that had two of these plus a Nanocomp in the loop of my Mesa/Boogie amp, where they worked well since the M/B FX loops (at least the ones I used) have solid-state sends. I had no luck using the Nanos in FX loops having vacuum-tube sends. No tap tempo.
That covers pretty much everything I own or have owned. I've tried a lot of others. Most of the boutique units that I've tried aren't (IMO) worth the inflated cost.