First of all, keep in mind that there is no uncontroversial classification of audio effects due to specific nature of those effects.
It particularly concerns audio equipment where one unit (effect) may influence on several audio characteristics at the same time – frequencies, dynamics, time and more.
Nevertheless we have to admit some generally accepted classification to be able to name things. Here is a simplified one. Audio effects are segmented usually to these 7 classes:
Since Ambient guitar tradition (if there is such a thing) puts no restrictions on characteristics of tone and due to experimental nature of this genre ambient guitarist should bear in mind relevance of all the effects mentioned above. It is a matter of taste, personal preferences and budget, of course, whether you should use specific audio effects or not.
There is one often discussed question: if we can substitute all those pedals with one guitar effects processor? The answer is: Yes and No. And that’s why:
These days some all-in-one units cope with guitar signal processing very well, even if we talk about simulation of complicated physical objects like amps. “Kemper Amps” is a good example. Some systems like Fractal Axe or Roland VG are fascinating. But they are not cheap! A basic ambient setup (delay + reverb + looper + volume pedal) with superb tone characteristics can easily fit in $500. Axe-Fx II XL+ Preamp/FX Processor close-out price is $1699, direct price is $2149.99.
Many guitar players assert without any qualification that processors sound “badly” or “unnatural”. Some cheap models really do, but I personally know guys who play ambient music using very affordable models like Boss GT-8 or Line 6 POD HD500 and these guys sound incredible! Remember, the most powerful musical tool is your mind and experience.
As far as it concerns my setup I had Roland VG-88, Roland GR-33 and Boss RC-50 loop station when I started playing Ambient music. No stomp-boxes. And I felt more than comfortable with them for a very long period of time. The reason why I decided to expand my setup was reaching the limits of this equipment and clear understanding of what I wanted to get from my future setup.
The obvious reason why pedal-boards are so popular is that you can replace any effect in the chain and leave the rest untouched. It happens that sometimes separate pedals are so unique that no processor can substitute them or the effects settings they provide might be more advanced, versatile and flexible.