It would be really useful to have a database containing various computations of (co)homology/homotopy groups of various spaces that arise in algebraic topology...
Note: There is so much known out there that one would have to first think really hard about how to organize it all.

Here's an example:
I could imagine that, for certain users, listing the first 30 integral cohomology groups of the spaces $K(\mathbb Z,1)$, $K(\mathbb Z,2)$, $K(\mathbb Z,3)$, and $K(\mathbb Z,4)$ could be more useful¹ than listing all the cohomology groups of all the $K(\mathbb Z,n)$'s. The reason is that, in order to do the latter, the information has to be packaged in a certain way that is probably not very easy to understand: the user would need to first unpack that information before she can access it.

¹ Of course, it's even better to have both pieces of information available.

It would be really useful to have a database containing various computations of (co)homology/homotopy groups of various spaces that arise in algebraic topology...
Note: There is so much known out there that one would have to first think really hard about how to organize it all.

Here's an example:
I could imagine that, for certain users, listing the first 30 integral cohomology groups of the spaces $K(\mathbb Z,1)$, $K(\mathbb Z,2)$, $K(\mathbb Z,3)$, and $K(\mathbb Z,4)$ could be more useful¹ than listing all the cohomology groups of all the $K(\mathbb Z,n)$'s. The reason is that, in order to do the latter, the information has to be packaged in a certain way that might be hard to understand: the user would need to unpack that information before she can access it.

¹ Of course, it's even better to have both pieces of information available.