For a long time the only block explorer for testnet has been the original blockexplorer.com, which is unfortunately often broken / behind / slow and not really maintained any more.
There is now a new one, here:
There's also a REST/JSON API for it.
Please note one curiosity of this block explorer is that the coinbase tx doesn't necessarily come first in the listing (it's sorted by "time received", see).
Other interesting thing to note: this site is built using bitcoinj. The author can be contacted on IRC sometimes using the nick damethos.