Though I personally tend to favour expository preaching in practice, topical preaching certainly has its place.
Scriptural Basis
A case could be made from Scriptural example...
Jesus's Preaching
Jesus's recorded preaching was purely topical - as far as I know, he never took a passage from the Old Testament and expanded on it. Rather, he chose topics that his audience needed to hear, and quoted various scriptures when relevant. For example, see the Sermon On The Mount
Disciple's Preaching
Like Jesus's preaching, records of the disciple's sermons were topical. They had in mind what they needed to talk about (preaching the Gospel, typically), and they used occasional Scripture references for support. In other words, their preaching was directed by the subject at hand (using Scripture as support), rather than being directed by a passage (expanding on applications of the passage).
For examples, see:
Letters to Churches
All though they are not strictly sermons, one might argue that the letters to the churches are quite analogous to sermons, and would have been sermons had the authors been among their recipients. As it is, all of the letters to churches are topical rather than expository. The argument could then be, since the goals of sermons and letters are the same: to correct doctrine, bring to maturity, encourage, etc, why should the content change simply because the medium changes?
Caveat...
But of course, we ought to keep in mind that when Jesus and the disciples preached, they were preaching something new, and didn't have much material to exposit. So these Scriptural examples should by no means be used to argue that preaching must be exclusively topical, but they do at least provide a basis for the acceptability of topical preaching.
Reasonable Basis
We think in topics
We think about things in topics. Whether we preach expositionally, or topically, we reduce things into topics naturally. Expository preaching is great, but say we want to know about a topic such as freedom in Christ from the law. Expository preaching will cover that when going through Romans, and also when going through Galatians, but a topical sermon on the subject drawing from a wide range of scriptures would greatly clarify and unify things.
Topics may need to be covered
It is often necessary to preach in order to meet a certain need. Perhaps there is high confusion about something, or perhaps a congregation simply needs to be brought onto the right track regarding an issue. If all sermons are simply systematically going through Scripture, then these needs will not be met (unless a topical sermon is interjected, and that is topical preaching).
Traditional Basis
In my opinion, tradition should not be taken into account as the basis for anything.
So, in conclusion, I think both have their place. One danger with topical preaching (and the reason why I prefer expository preaching) is that it tends to be more eisegetical, as preachers tend to subtly twist Scriptures to fit their arguments. This is a mistake, and while it is not a fundamental part of topical preaching, it does tend to occur in practice.
