I'll add to the chorus: The FRCS, and maybe the PGtF, are the only must-haves.
But every other book (with the notable exception of Champions of Ruin) is really neat, too, so if you want more, by all means go and get it:
Silver Marches, Unapproachable East, Shining South: Those are pure regional books, detailing the areas in question. Very recommended if you want to place your campaign in the respective area.
Underdark: Sort of regional supplement, but since the Underdark is not just another country, the differences between the Underdark and the surface are detailed as well. If you want to play an underdark campaign, this is highly recommended, and it's not bad even if you just want to go there for some time.
Magic of Faerûn: Well, you know that one. Realmsian magic.
Races of Faerûn: Goes into larger detail about all the major races that poplulate the continent. There are several additions to those in the FRCS, like Avariel (Winged Elves), Urdunnir (Dwarves with an even greater affinity for stone), Forest Gnomes, as well as two new special kinds of Tieflings: Fey'ri (descendants of unholy unions between gold elves and succubi) and Tanarukk (demonic orcs). There's also stuff about minor races (Like goblinoids or kir-lanan).
Faiths and Pantheons: A book about the gods: The "major deities" (those who got more than a table entry in the FRCS) get expanded information, including deity stats, and the rest get entries comparable to those from the major deities in the FRCS. Also, there are religious PrC's and other stuff.
Serpent Kingdoms: This is a mix of racial and regional book. It is all about reptilian races, including Naga, Yuan'ti, and the Sarrukh - one of the Creator Races, who created all the Serpent People.
Lords of Darkness: 28 evil organizations, from the infamous Zhentarim to the Twisted Rune. 7 are considered "major" and get more detail.
Monster of Faerûn: A little on the expansive side (though you can probably get it at a large discount), it has more monsters - mostly ones that are legendary Realmsian beasts, like the Sharn or the Phaerimm.
Waterdeep: A city sourcebook. The City of Splendours in all its splendour. Not exactly like the area supplements, as it is all about this one city. A lot of info about the city layout, its history, major personalities and power groups, dangerous locales (foremost Skullport and Undermountain, of course). Also includes stuff like "where can I get info about this or that topic?" or "where can I buy or sell what sort of goods?"
Lost Empires of Faerûn: One of the best supplements I have come across, and I mean not only in regards to the realms. This book describes the legendary nations and kingdoms you always read and hear about when you wander the Realms: Cormantyr, Netheril, the High Forest, and all about the God-Kings of the East and the infamous Crown Wars where the elven nations fought each other for 3000 years.
