I just got the Forgotten Realms D&D Archives 1-3 and was wondering if I should play them in a certain order? I played Eye of the Beholder for a few minutes and liked it, but if the story connect in some way I won't mind playing them in order (if they even have one)?

Each of the series (ie "forgotten Realms", etc.) stand alone. The 4 Pools games have an order and then the Savage Frontier pair have an order but they're separate from the Pools series..

This post may help:

https://www.gog.com/forum/general/dd_ideal_play_order_gold_box_infinity_etc/post4

I believe the Pools games are in the second collection.

Hope this helps

edit: Interesting backstory on these. PCGamer says GoG owns the games outright now:

http://www.pcgamer.com/how-gog-rescued-13-forgotten-realms-games-from-licensing-hell/

I know PCGamer has some issues enough to take anything that they say as 100% gospel but it would be interesting if that was true..

In general I believe that it always make sense to play in chronological order and to stick with one series at the time.

Forgotten Realms: The Archives - Collection Two
• Hillsfar (1989)
◕ Pool of Radiance series
• Pool of Radiance (1988)
• Curse of the Azure Bonds (1989)
• Secret of the Silver Blades (1990)
• Pools of Darkness (1991)
• Forgotten Realms Unlimited Adventures (1993)
◕ Savage Frontier series
• Gateway to the Savage Frontier (1991)
• Treasures of the Savage Frontier (1992)

Forgotten Realms: The Archives - Collection One
• Eye of the Beholder I (1991)
• Eye of the Beholder II (1991)
• Eye of the Beholder III (1993)

Forgotten Realms: The Archives - Collection Three
• Dungeon Hack (1993)
• Menzoberranzan (1994)

Dungeons & Dragons: Ravenloft Series
• Ravenloft: Strahd's Possession (1994)
• Ravenloft: Stone Prophet (1995)

Dungeons & Dragons: Krynn Series
◕ Dragonlance series
• Champions of Krynn (1990)
• Death Knights of Krynn (1991)
• The Dark Queen of Krynn (1992)

Dungeons & Dragons: Dark Sun Series
• Dark Sun: Shattered Lands (1993)
• Dark Sun: Wake of the Ravager (1994)

Forgot to mention that there's a few addon helper programs that run with those games. May help you with things like mapping.

We discuss one of them here:

https://www.gog.com/forum/forgotten_realms_collection/ive_found_the_gold_box_companion_pretty_vital/page1