What sort of thing?

Solution 1:

Depending on the thing(s) in question, it's either

This sort of thing is...

or

These sorts of things are...

You need (pro)noun/verb plural agreement.

Samples:

Yesterday I slipped on the ice. Today I slipped on a sliver of soap. This sort of thing is always happening to me.

Last week I needed stitches from a shaving accident. Yesterday I slipped on the ice. Today I got hit by a car. These sorts of things are always happening to me.

Solution 2:

Both of these work and are idiomatically proper in English:

These sorts of things are ...
This sort of thing is ...

"This sort of things is ..." doesn't follow the typical idiom.
"sort of things" and "sorts of thing" are both unusual and probably better avoided.

As @Hellion's examples show, the choice of the workable phrase will be roughly determined by the number of the things in question.