I also think they are incredibly interesting

This is a rundown of the major accent families, I guess you could call them, that are spoken in Belgium and the Netherlands. Keep in mind that along the BE-NL border, the accents are often similar if not the same. This is a very unconventional summary of the difference accents and ignores a lot, but is however a good introduction to the major accent groups without going into never-ending detail:
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1. North and North Eastern accents (Friesland, Groningen, Drenthe, Overijssel, some parts of Gelderland) - They have been influenced heavily by Frisian and Niedersaksich. There is much variation between the various accents within this region, but they are on a continuum with shared characteristics. One of the most well known aspects of this dialect groups is their pronunciation of the final -n. For instance, it is common in these accents to say "werk-n" where most accents in Belgium and Netherlands tend to say "wer-ke" in informal situations. They speak with a hard G, but something softer than with Hollands. These accents also tend to say their Ws like a V.... although it is actually not a V, it often sounds like one to non-native speakers.
2. Hollands/Randstad accents (North Holland, South Holland, Utrecht)- This is the accent that most people are familiar with. Hard, throaty harsh Gs, sometimes an overexaggerated final R (the "Gooise R" often sounds like a stretched out American R), and diphtongization of certain vowels (Owpa instead of Opa, as pronounced in the more conservative accents) are some of the characteristics of these accents. Of course, there is much variation in this group as well. These accents also tend to say their Ws like a V.... although it is actually not a V, it often sounds like one to non-native speakers. To give some socio-cultural-linguistic input, Hollands is by far the most dominant of accents. To some speakers of other accents (especially in the South of NL and Belgium), it can sound irritating, loud, pompous and annoying. Although, there many native speakers that enjoy this accent as well.
3. The Brabantic accents - This accent group crosses borders between BE and NL and has been historically one of the strongest and largest influences on the Dutch langauge at various points in history. Although there is extreme variation in this group of accents, Brabantic characeristics can be found in Noord Brabant (NL), Antwerpen (BE), Vlaams-Brabant (BE) and Brussels. One of the most well known aspects about these accents is the use of "gij" which is an enduring feature from historical forms of Brabants. Most of the Brabantic accents speak with a soft g, and most speak with a trilled-R although many Brabantic accents in Netherlands speaks with a French R (see Limburgs). These accents mostly say their Ws like, well, a W. It sounds like an English W, but without so much rounding of the lips. Brabants and Limburgs are considered "conservative" accents, in that they retain certain aspects of pronunciation or grammar which have been abandoned or changed by other accents, like Hollands. This sometimes makes these accents sound older or more traditional to native speakers of other accents.
4. Limburgs- These accents are spoken in Belgian and Dutch Limburg. I happen to speak with this accent and personally think it is the most beautiful accent in the lowlands and many native Dutch speakers agree. However, Limburgs is often made fun of because of its quite eccentric pronunciation. Limburgers are typially portrayed as speaking very slowly, stretching vowels and using a very bouncy, sing-songy and often whiny intonation (especially in the South of Dutch Limburg). This last characteristic comes from they fact that langauge of Limburgs is one of the few western languages that has aspects of tonal speech: the tone in which a word is said can sometimes change meaning. One of the other characteristics of Limburgs is the use of the French-R. All people who speak with a Limburgs accent speak with this R. For instance, the first R in the word "radar" is spoken with a uvular trill and the final R is spoken with a uvular fricative, kind of like how a French person says their Rs. I don't understand why, but this R creates confusion for speakers of other accents at times. My friend Bart, a South-Limburger, often has to spell his name to people in Utrecht, where he lives, because they think that his name is "Bagt." Limburgers speak with a soft G, although they sometimes have a "windier" G than other speakers of the soft G due to later voice onset than in other accents. Limburgs uses the same W that Brabants uses.
5. Flemish accents - East and West Flanders in Belgium - This accent group is very interesting but one of which I know very little. Maybe one of the members on this board could fill in some of the blanks. In short, one of the most recognizable characteristics is their pronunciation of the letters G and H. They H tends to disappear and they said their Gs as Hs. So, for instance, the word "Beginner" turns into 'behunner". They speak with a trillende tongue R.
Of course, this summary leaves out a lot of variation and even a few accent groups, but these are the major groups that are commonly discussed and referred to in popular culture and amongst native speakers. This has only been a run down of how they speak "standard" Dutch. This doesn't take into account the differences in Belgian and Dutch Dutch within these accent groups. This also has not taken into account various dialects that are still spoken, city dialects (like Maastrichts), or minority langauges (like Frisian, Flemish, Limburgs).
So, enjoy all the variation! It's what makes the langauge beautiful (...at times, depending on the accent

).