What is the cleanest way to ssh and run multiple commands in Bash?

To match your sample code, you can wrap your commands inside single or double qoutes. For example

ssh blah_server "
  ls
  pwd
"

Edit your script locally, then pipe it into ssh, e.g.

cat commands-to-execute-remotely.sh | ssh blah_server

where commands-to-execute-remotely.sh looks like your list above:

ls some_folder
./someaction.sh
pwd;

How about a Bash Here Document:

ssh otherhost << EOF
  ls some_folder; 
  ./someaction.sh 'some params'
  pwd
  ./some_other_action 'other params'
EOF

To avoid the problems mentioned by @Globalz in the comments, you may be able to (depending what you're doing on the remote site) get away with replacing the first line with

ssh otherhost /bin/bash << EOF

Note that you can do variable substitution in the Here document, but you may have to deal with quoting issues. For instance, if you quote the "limit string" (ie. EOF in the above), then you can't do variable substitutions. But without quoting the limit string, variables are substituted. For example, if you have defined $NAME above in your shell script, you could do

ssh otherhost /bin/bash << EOF
touch "/tmp/${NAME}"
EOF

and it would create a file on the destination otherhost with the name of whatever you'd assigned to $NAME. Other rules about shell script quoting also apply, but are too complicated to go into here.