These are the top 10 analog delays.
Of course this ranking is absolutely subjective.

1. Electro Harmonix – Deluxe Memory Man

There are copious versions of the Deluxe Memory Man. With the famous Electro Harmonix “Big” enclosure, with the smaller XO enclosure, with and without tap tempo but one thing always stays the same: its striking percussive sound. Although the DDM is an analog delay, its unique sound offers trebly repeats and a kind of modulation that somehow seems to be organic. It is and remains a classic that every delay loving guitarist should have played at least once in his life.
Click here for a video of the Electro Harmonix – Deluxe Memory Man.

2. Boss – DM-2

With its three knobs (repeat, echo, intensity) and 300ms maximum delay time the Boss DM-2 is a one trick pony – but it masters this trick perfectly. As a slapback delay it fits completely into the sound and thickens the guitar signal. There is no better delay for this purpose.
The recently debuted reissue provides an additional custom setting with an extended delay time.
Click here for a video of the Boss – DM-2.

3. Chase Bliss Audio – Tonal Recall RKM

I think there is no other analog delay that creates more flexible and bizarre sounds like the Chase Bliss Audio Tonal Recall RKM.
Something special is its “digital brain” which can be controlled by little dipswitches via expression pedal or midi. Despite its pure analog signal processing this “digital brain” allows a multifarious modulation. The sound of the Tonal Recall RKM is marvelous and because of the small enclosure it only needs little space on the pedalboard. What more do you need?
Click here for a video of the Chase Bliss Audio – Tonal Recall RKM.

4. Moog- Moogerfooger MF- 104M

In the course of the company history Moog also produced (limited) delays which recent versions can be controlled via midi and tap tempo. And of course many parameters can also be controlled by CV (control voltage). The sound of the MF-104M is unique and the built in pre-amp allows to create clean as well as dirty and boosted sounds. The minifooger series also offers a similar sounding delay without modulation.
Click here for a video of the Moog- Moogerfooger MF- 104M.

5. DOD – Rubberneck

Although the DOD Rubberneck has been debuted this year it has yet become a classic. Its sound is oriented to the previous model – the DOD 680 Analog Delay. The sound is a more dirty and with the gain pot you can add some extra dirt.
The new developed rubbernecking enables you to experiment and create totally new kinds of delay sounds.
Click here for a video of the DOD – Rubberneck.

6. Diamond Memory Lane 2

The closing of the production of MN3005 chips caused the end of the manufacturing of the Diamond Memory Lane 2. But nevertheless this delay with two presets and foot-controlled modulation is absolutely recommendable. Its sound is darker and can be variated by using the tone pot.
Click here for a video of the Diamond Memory Lane 2.

7. AnalogMan ARDX20

The sound of the AnalogMan ARDX20 is based on the legendary Ibanez AD9 delay which has been debuted in the 1980s. But it has got an extended maximum delay time and provides the opportunity to choose between two delay settings via foot switch. By adding the Amazeo (which is supposed to come out as a smaller version next year) you will also get tap tempo, different kinds of modulation and the possibility to save presets.
Click here for a video of the AnalogMan ARDX20.

8. MXR Carbon Copy

The MXR Carbon Copy is a workhorse and can be found on uncountable pedalboards. Its sound fits perfect into the guitar signal – similar to the sound of the Boss DM-2 – but the Carbon Copy also offers modulation and an extended delay time.
The Deluxe Version, which has been debuted recently provides tap tempo and the possibility to chose between the classical Carbon Copy sound and a bright version.
Click here for a video of the MXR Carbon Copy.

9. Ibanez AD Series

The extensive Ibanez AD Series (AD-9, AD-80, AD900, AD999, AD999pro, AD9pro, ADmini) as well as the Maxon delays (which are built up identically) are produced since the 1980s. Although the maximum delay time varies, every version shows the typical Ibanez AD Sound. They are perfect to thicken solo sounds or as a warm delay. I think in the diversity of good sounding models every guitarist should find a suitable one.
Only a version with modulation is missing yet.
Click here for a video of the Ibanez AD.

10. Way Huge Aqua Puss

One can say that the Way Huge Aqua Puss is the boutique version of the Boss DM-2 on which it is based. Way Huge developed this pedal to emphasize the virtues of the DM-2. With the Echo Puss and the Supa Puss Way Huge extended the series by models with modulation and tap tempo.
A video of the Way Huge Aqua Puss is coming soon.