Standard Nintendo DS / DS Lite: No. No browser, no Wi-Fi web access.
Nintendo DSi / DSi XL: Limited.
m.wikipedia.org, textise.net).Nintendo 3DS / 2DS / New 3DS: Has a **much better** NetFront-based browser (supports HTML5, JS, video). Still slow, but usable for wikis, guides, forums.
Recommendation: Use a smartphone, tablet, or PC for the web. The DSi/3DS browser is a novelty/emergency tool only.