Lane’s Arabic – English Lexicon, has been unequaled since 1863, despite the fact that it only runs to qāf. Roots that start with a letter after qāf are present, but the entries are not complete.
There are two ways to access Lane online.
1. On Perseus, Lane is available in full text. I have not checked the accuracy of it.
2. On Tyndale, a page-per-page scan is available, fully indexed. I like it a lot.
3. Bonus. If you want to have a scan of Lane yourself, download away:
Lane’s Lexicon is especially useful for literary texts.