There are two somewhat different things that one could want here: (A) a web site that gives conjugations of verbs, or (B) a more compact tabulation that only gives the principal parts.
The cactus2000.de site looks like A for Latin. For this purpose, here are the two web sites that I have found the most useful in Greek:
Wiktionary generally does a pretty good job of presenting the standard Attic forms, and it usually also gives a selection of epic forms as well. For a some of the more obscure verbs it doesn't have conjugation data, and it also doesn't give every obscure or dialectical form of every verb. I think it's implemented using some hybrid of human decision-making and computer algorithms. Whatever the details of how it works, I've never seen an outright error. They usually seem to do a pretty decent job of deciding which forms are the main and most important forms. You need to be aware of certain facts in interpreting their information, e.g., that Homer doesn't always use the augment.
U Chicago Morpho is more like a raw dump of every form of the verb found in some big corpus (Perseus?) that covers a lot of dialects and periods and has been tagged by humans. So, e.g., for φημί they list 42 forms in the present active indicative. Forms with elisions, Doric and Ionic forms, it's all there in a big blob. The advantage is that there is no risk of seeing a false picture that is just what someone thinks is or is not a real form of the verb.
For B, a concise tabulation, it's a little more complicated to define how this should be done. I've spent a fair amount of time doing this for a couple of projects of my own: an attempt to present the Iliad in an innovative way, and a grammar practice video on the principal parts in the Homeric dialect. It's not really possible to completely define a list of "the" six principal parts of Greek verbs. Frequently there are multiple alternative forms of one of the principal parts, even within the same text. Many verbs lack some of the principal parts, or they're unattested. For example, of the verbs I've looked at for my project, roughly 3/4 do not have a future tense attested in Homer. If you look at these on wiktionary, you'll find that they either supply an attested Attic form, or if there's a separate conjugation table given for the Homeric dialect, their algorithm will have supplied what it thinks is the plausible future.
Since Homer is the dialect I'm working on, I wrote a script that goes through the Project Perseus treebank and prints a tabulation of all the inflected forms of a given word. So for instance, when I was trying to tabulate the first three principal parts of ἀείδω, I used this command:
report_inflections.rb tense=pfa mood=i voice=a number=* person=* ἀείδω
The output was this:
person = 1
person = 2
person = 3
tense = f
person = 3
The given lemma ἀείδω is an exact and unique match to the database, including accentuation.
total matches: 4, total occurrences: 5
So this tells me that the first and third principal parts of this verb are ἀείδω and ἄεισα (inferred from the form that actually occurs, ἄεισε). It also tells me that there is no future attested in Homer. So now what is the right thing to do for this dialect? I can look on wiktionary and see that this verb does actually seem to have had a future tense in ancient Greek, but that the situation is complicated. They list three possibilities, ἀείσω, ᾄσω, and ᾅσομαι, and they tell you very briefly about their usage -- it sounds like the middle may be used instead of the active, but, I assume, with the active meaning.
So if you want a brief tabulation of the principal parts of some list of verbs, such lists are certainly out there, but they're going to be per-dialect, and they'll either be messy or else, if they look suspiciously complete and tidy, you should realize that they are probably hiding a ton of information from you.
Also keep in mind that there will sometimes be both a first aorist and a second aorist.
If the idea is that you want to compile flashcards for yourself, then I think you'll find that it's quite a laborious and time-consuming process to curate a big list for a particular dialect, so you probably do want something of flavor B. For the Homeric dialect, I have a decent-sized compilation here. Within the file for each verb, the "princ" field contains the second and third principal parts. Here is a web site that gives a table for koine.