There would be a few I would bring back. 

The X5 /231 services Hartlepool - Newcastle.  Especially with bad the trains are under northern Hartlepool needs a service to Newcastle again and I think if done right it could successful.  I know Stagecoach tried recently with the X55 but that was never going work due the Times been all wrong and been infrequent.  Same with the X11 that go north east  tried a few year before that was not frequent enough or advertised to let people know plus both where Saturday only services.  A Monday - Saturday regular express service would work.  

H1 Hartlepool - North Tees Hospital 
Hartlepool desperately needs a proper regular bus service to North Tees Hospital if the Trust are going to continue to services there.  Going to Hartlepool Hospital to get the shuttle bus ( which is usually a spare bus Boro taxis or 23 Taxis have ) or getting the 36 to Stockton then 37 or 59 not good enough and takes to long.   

236 Hartlepool - Bishop Auckland 

Even though it took a while to get there was a decent bus ride which I used to enjoy plus would link Sedgefield with Hartlepool again giving people there an extra option.  

87 Hartlepool - Hartburn.  

Was short lived and obviously the company no longer exists but was a nice alternative to the 36 to get to Stockton.  

X24 Hartlepool - Darlington.  

Again short lived and not sure how many of you remember this service as never lasted very long but was a good idea and worth trying it again as a regular service.  

Service 10 Hartlepool Headland - Middlesbrough.   Would need to be re numbered but a good idea a fast service between Hartlepool and Middlesbrough would take pressure off the 36 and provides an alternative to the 7 between the Headland and Hartlepool Town Centre.