With Christmas fast approaching, the most important thing to know is that Nintendo DSi consoles are region-locked, meaning they will only play Nintendo DS games that are licensed for the same region. For example, assuming you own a genuine UK version of the DSi, then only UK licensed software will work on your console.
Previously DS Lite consoles were NOT region-locked and you could buy any game from any region. Typically on eBay UK, there are sellers both in the UK and elsewhere listing stock sourced from the US or Far East, often at a much lower price than the genuine UK article.
If you own a DSi console, or are thinking about getting one, or buying games for someone who does, to avoid disappointment this Christmas, you should ensure that you buy the correct games,
For buyers in the UK, the packshots should all display the PEGI (EU) or BBFC (UK) ratings. The PEGI ratings show the recommended minimum age suitability of the game, i.e. 3, 7, 12, 16 or 18. The BBFC ratings are the same as the cinema ratings in the UK, i.e. U, PG, 12, 15, or 18. The imports (that won't work) have a letter, such as E, M, T or R and these are the ESRB (US) ratings.
However, it's probably a good idea not to go on the packshot alone, the location of the seller is also useful. A seller from Hong Kong or the US is unlikely to be selling UK stock, but on the other hand, there are UK sellers that sell imported stock.
Overall, the seller should state in the item title and/or listing that the game is suitable for DSi consoles as well as DS/DS Lite ones, and ideally display the correct packshot to assist the buyer. A good indication would also be the price, especially of new releases. If the game is much cheaper than others, it's unlikely to be the genuine article. But if you're not sure, ask before you buy.