Note: The following comments were first posted to the reformed-epistemology discussion group in July 2001, in response to a query about the main areas of agreement and disagreement between these two Christian thinkers. I have corrected a few typos, made some minor changes of wording, and added relevant hyperlinks. The original post is archived here.
Both men acknowledge Jesus Christ as Lord and Saviour. A obvious and unsophisticated point, but important nonetheless. Praise God that He has directed two such great intellects (and humble spirits) in the service of the Kingdom.
Both men have emphasised the determinative relationship between metaphysics and epistemology, i.e. that a good theory of knowledge requires a certain theory of reality. Indeed, both have gone so far as to argue (albeit by different routes) that a specifically theistic framework is necessary for human knowledge to obtain — although Plantinga has been more reserved in the statement of his conclusions than Van Til.
As a correlated point, both have argued that a naturalistic metaphysic leads to a debilitating skepticism in epistemology.
Van Til argued passionately against the idea of epistemological autonomy, i.e. the suggestion that disagreements between believers and unbelievers can be settled by an appeal to 'religiously neutral' principles of reason. It seems to me that Plantinga would concur with this position (see, e.g. his closing comments in 'Reason and Belief in God' to the effect that "there is ... disagreement in the first place [between theist and nontheist] as to what are the deliverances of reason"), although it certainly doesn't feature as prominently in Plantinga's work as in Van Til's.
In a similar vein, both have argued that the Christian philosopher ought not to ply his trade from a position of pretended autonomy or neutrality, as if that were a prerequisite of participation in the broad philosophical community. On the contrary, Christian philosophy should be conducted (unashamedly) within the bounds of, and building upon, Christian doctrinal/doxastic commitments. On this point see Van Til, passim, and Plantinga, esp. 'Advice to Christian Philosophers'.
Both men endorse (in general terms) Calvin's view of the sensus divinitatis — the innate knowledge (or disposition to knowledge) of God implanted in the human mind. As such, both hold to the 'proper basicality' of belief in God: theistic belief can be warranted for a person (and, in the 'normal' case, should be warranted) even in the absence of reasons, evidential support, explicit arguments, etc. based on other items of knowledge. (But see below for some differences.) Thus, both firmly reject the idea that rational theistic belief must be supported by a foundation of other more fundamental (and allegedly less controvertible) beliefs.
Both have been critical of the project of natural theology, in part because of the myth that good theistic arguments are necessary for rational theistic belief, and in part because both thought that the traditional arguments for God's existence were poor or outright fallacious. (However, see below for some differences in their motivation for these criticisms.) Plantinga has warmed to natural theology in more recent years (compare 'God and Other Minds' with his lecture 'Two Dozen (or So) Theistic Arguments'), and some Van Tilians likewise (notably, John Frame). It is a popular misconception that Van Til rejected in principle the formulation of theistic arguments (or non-transcendental theistic arguments), but see the correctives here
Plantinga's work stands squarely in the Anglo-American analytic tradition, whereas Van Til's work is characteristically framed in the conceptual apparatus and terminology of Continental idealist thought. (This latter fact partly explains the neglect and superficial dismissal of Van Til's work among contemporary Christian philosophers, although a number of Van Til's students — notably Frame and Bahnsen — have done much to translate his thought into a more 'palatable' form.) [Of course, this point is not so much a disagreement as a difference in approach.]
Also on the subject of style (yet with implications for substance), Plantinga's work is characterised by exhaustive (and, for some of us, exhausting!) analytic detail, with meticulously formalized arguments, while Van Til paints in broad philosophical strokes with an eye for 'the big picture' — leaving the details for others, more so inclined, to fill in. (William Lane Craig, unfairly in my opinion, wrote than Van Til was "not a philosopher" on account, apparently, of this difference between the two men.)
Van Til and Plantinga evidently disagree on the nature of human freedom and the extent of divine sovereignty. Van Til follows the Westminster Confession of Faith, III & IX, on this point and is thus committed to a compatibilist view of human freedom. Plantinga, on the other hand, is firmly persuaded (more on the basis, I'd venture, of philosophical considerations than biblical ones) that a libertarian, incompatibilist position is correct. This is no small point, for the work of both men has been profoundly influenced by their views on this matter. For example, Van Til contends that God's comprehensive pre-interpretation, and therefore pre-determination, of creation history (including free human actions) is a precondition of its intelligibility (for those of us created "to think God's thoughts after Him"). Plantinga's classic Free Will Defence (against the deductive atheistic argument from evil) and his work on reconciling divine foreknowledge with free human acts (see 'On Ockham's Way Out') both presuppose a libertarian conception of human freedom.
While both have been critical of natural theology, Van Til's complaints have been driven primarily by a concern about the influence of commitments to (or pretensions of) intellectual autonomy and neutrality in the formulation of theistic arguments, the presentation of Christian evidences, and the development of Christian apologetic methodologies in general. Plantinga's objections, on the other hand, have been more motivated (at least in his early work) by skepticism about what the 'classical arguments' achieve and by his views, much influenced by the Reformed tradition, concerning the proper basicality of theistic belief (which suggest that natural theology is at best superfluous and at worst impious).
Van Til championed the use of a transcendental form of argumentation as the only method capable of rationally, objectively and decisively adjudicating between philosophical systems with conflicting presuppositions (with regard to the nature of reality, the nature of God, the nature of man and his intellect, ultimate epistemic authorities, etc.). As a result, Van Til glories in what he takes to be the unavoidable element of circularity and precommitment in Christian theistic apologetics, not to mention the striking correlative conclusion that "antitheism presupposes theism". Plantinga's published works, as far as I know, have made no explicit use of (or even commented on) transcendental argumentation in the apologetic cause (although his 'evolutionary argument against naturalism' is arguably in the spirit, if not the letter, of the negative transcendental critiques prominent in Van Tilian thought). I think this is a point where there could (and should) be much more fruitful dialogue between Van Tilians and Plantingans, once prejudices and misconceptions on both sides have been laid to rest.
Van Til put a considerably greater emphasis on the radical antithesis between the believer and the unbeliever with respect to epistemic and ethical norms (although the fact that Van Til saw this antithesis as one of principle rather than practice is often neglected even by his would-be advocates, to the detriment of the Van Tilian cause). From my reading of Plantinga, I surmise that he would endorse this perspective to a point, but would by no means be comfortable with Van Til's more extreme formulations of the matter. (I make no comment here on the motivation of either party for their positions on this vexed issue!)
While there is much commonality between Van Til's view of Christian theistic belief as 'presuppositions' and Plantinga's 'properly basic beliefs', Van Til invested 'presuppositions' with considerably more significance. For example, Van Til attached a strong ethical component to such beliefs (consider his 'covenant-keeping/covenant-breaking' motif; cf. also Frame's exposition of presuppositions as 'basic heart commitments') and also viewed them (or at least a significant subset) as possessing transcendental necessity, i.e. as being necessary preconditions of rational inquiry and debate.
Finally, it appears that Van Til and Plantinga have slightly different understandings of the sensus divinitatis. Van Til, placing much emphasis on a popular Reformed interpretation of Romans 1, apparently sees this as actual knowledge of God — present in every human being, suppressed in sin but ultimately ineradicable, and thus supplying the universal 'point of contact' for the apologist. For Van Til, then, every unbeliever knows God (despite their profession) at a fundamental, deep-rooted, but potentially accessible level. Plantinga, however, seems to conceive of the sensus divinitatis less strongly; as an intellectual faculty or disposition toward belief in God, whereby warranted belief in God is generated in certain appropriate (and probably commonplace) circumstances. Thus, Plantinga (as I understand him) would not go so far as to say that every person knows God (whether in principle or in practice), only that every person possesses a natural and normative God-given disposition toward theistic belief, the effect of which has been considerably distorted by sin such that not every person actually believes. (This common acknowledgement of the noetic effects of sin suggest another point of agreement between the two: both recognise the necessity of divine grace in human knowledge of God, and the necessity of full-blown regeneration for saving knowledge, although again Van Til makes much more of this than Plantinga. I leave for another time the question of whether this implies or requires a Calvinist soteriology on Plantinga's part...)
 My friend Paul Martin has since pointed out to me that, strictly speaking, the FWD does not presuppose the actuality of libertarian freedom, merely its possibility. He is quite correct. For some qualifying remarks, however, see here and also Paul's follow-up post.