When it comes to adapting The Lord of The Rings, Tom Bombadil has a habit of not making the cut.
Are there any adaptations that do feature him?
More than you might think, though most of them are video games only tangentially related to The Lord of the Rings novels.
In no particular order:
The 1955 BBC radio series. This one had the distinction of being heard by Tolkien, who didn't care much for Bombadil's voice actor:
I think the book quite unsuitable for 'dramatization', and have not enjoyed the broadcasts - though they have improved. I thought Tom Bombadil dreadful - but worse still was the announcer's preliminary remarks that Goldberry was his daughter (!), and that Willowman was an ally of Mordor (!!)
The Letters of J.R.R. Tolkien 175: To Molly Waldron. November 1955
The 1992 Tales of the Perilous Realm, a BBC Radio dramatization of some of Tolkien's lesser-known poems, and the Bombadil segment of Fellowship of the Ring
War in Middle-Earth, a 1988 video game released on early PCs (including the Commodore 64 and the ZX Spectrum)
1 For the unitiated, the gist of the LEGO X games is that the plot of the work being adapted is divided into a small number of playable levels, separated by an overworld. You play each level with the characters canonically present for the events it depcits, and after completing a level you're allowed to replay it with any characters you've unlocked. Some characters are unlocked by playing the levels in story mode, but some (like Bombadil) are just standing in the overworld and have to be purchased with the in-game currency
2 I don't even have a witty remark to that. Just...what?
3 Thanks to Jörg W Mittag for pointing this one out in comments
4 Thanks to Ian Thompson for pointing this one out