There are MANY different types. Here are a few with links to their site and/or an explanation of the program. These programs can change. So, make sure you are looking at the most recent information/publications. The programs/links are current as of the day of this post.
Mortgage Loan Modification Program Options
FHFA (“Federal Housing Finance Agency”) Streamlined Modification
http://www.fhfa.gov/webfiles/25068/StreamlinedModInit32713Final.pdf
Streamlined Modification (Fannie Mae GSE)
https://www.fanniemae.com/content/announcement/svc1305.pdf
Streamlined Modification (Freddie Mac GSE)
http://www.freddiemac.com/singlefamily/service/streamlined_modification.html
Federal MHA (“Making Home Affordable”) Options – All
http://www.makinghomeaffordable.gov/programs/view-all-prgrams/Pages/default.asp
HAMP Tier 1 (non GSE)
https://www.hmpadmin.com/portal/learningcenter/docs/presentations/mhaservicerwebinar_stdaltwtrfall_presentation.pdf
HAMP Tier 2 (non GSE)
HAMP PRA (Principle Reduction Alternative)
http://www.makinghomeaffordable.gov/programs/lower-paymets/Pages/pra.aspx
HAMP (nonGSE) 2MP (2nd Lien Modification Program)
http://www.makinghomeaffordable.gov/programs/second-mortgage-help/Pages/default.aspx
HAMP (Fannie Mae GSE)
HAMP (Freddie Mac GSE)
http://www.freddiemac.com/singlefamily/service/mha_modification.html (Note: No Tier 2)
FHA-HUD HAMP
http://portal.hud.gov/hudportal/HUD?src=/hudprograms/fhahamp
http://www.makinghomeaffordable.gov/programs/lower-payments/Pages/fha-hamp.aspx
FHA-HAMP Second Lien Program (FHA2LP)
http://www.makinghomeaffordable.gov/programs/lower-rates/Pages/fha2lp.aspx
VA HAMP
http://www.makinghomeaffordable.gov/programs/lower-payments/Pages/va-hamp.aspx
USDA HAMP
http://www.makinghomeaffordable.gov/programs/lower-payments/Pages/rd-hamp.aspx
HAUP (Home Affordable Unemployment Program)
http://www.makinghomeaffordable.gov/programs/unemployed-help/Pages/up.aspx
“IN HOUSE” Modifications
These are modifications offered by individual entities. You have to ask them for information on their particular program. Many mimic the HAMP program.
Mortgage Loan Refinance Program Options
HARP (“Home Affordable Refinance Program”)
http://www.makinghomeaffordable.gov/programs/lower-rates/Pages/harp.aspx
HARP (Freddie Mac – GSE)
http://www.freddiemac.com/mortgage_help/harp.html
HARP (Fannie Mae – GSE)
https://www.fanniemae.com/content/faq/harp-du-refi-plus-faqs.pdf
FHA Short Refinance
http://www.makinghomeaffordable.gov/programs/lower-rates/Pages/short-refinance.aspx
Refinance
All the other usual options with the existing lenders in the market