Since I'm most familiar with 10.1+, and cursors in general are a lot better in the da module, here's a potential solution. Currently, you are creating a cursor each time you change fields, which means you are taking a hit there. Furthermore, you are checking the field type for each record instead of just using the field type once to filter initially.

I've changed how Null values are checked, but I haven't thoroughly tested it to check for all possible values. For the small sample dataset I had, it worked @ 10.2.2.

#Return None if the value needs to be changed, else return the value
def nullify(value):
    x = value    
    if value is not None: #True null fields are read as None types
        if type(value) == str:
            if value.lstrip(' ') == '' or value.lower() == '<null>':
                x = None
        else: 
            if value == 0:
                x = None 

return x

#We're only interested in some fields
ftypes = ("String", "SmallInteger", "Integer", "Double")
fieldList = [f.name for f in arcpy.ListFields(fc) if f.type in ftypes]

with arcpy.da.UpdateCursor(fc, fieldList) as rows:
    for row in rows:
        vals = [r for r in row]
        nulled = map(nullify, vals)
        if vals != nulled: #Only update if the row actually needs to be changed.
            rows.updateRow(nulled)

Since I'm most familiar with 10.1+, and cursors in general are a lot better in the da module, here's a potential solution. Currently, you are creating a cursor each time you change fields, which means you are taking a hit there. Furthermore, you are checking the field type for each record instead of just using the field type once to filter initially.

I've changed how Null values are checked, but I haven't thoroughly tested it to check for all possible values. For the small sample dataset I had, it worked @ 10.2.2.

#Return None if the value needs to be changed, else return the value
def nullify(value):
    x = value    
    if value is not None: #True null fields are read as None types
        if type(value) == str:
            if value.lstrip(' ') == '' or value.lower() == '<null>':
                x = None
        else: 
            if value == 0:
                x = None 

return x

#We're only interested in some fields
ftypes = ("String", "SmallInteger", "Integer", "Double")
fieldList = [f.name for f in arcpy.ListFields(fc) if f.type in ftypes]

with arcpy.da.UpdateCursor(fc, fieldList) as rows:
    for row in rows:            
        nulled = map(nullify, row)
        if row != nulled: #Only update if the row actually needs to be changed.
            rows.updateRow(nulled)

Since I'm most familiar with 10.1+, and cursors in general are a lot better in the da module, here's a potential solution. Currently, you are creating a cursor each time you change fields, which means you are taking a hit there. Furthermore, you are checking the field type for each record instead of just using the field type once to filter initially.

I've changed how Null values are checked, but I haven't thoroughly tested it to check for all possible values. For the small sample dataset I had, it worked @ 10.2.2.

#Return None if the value needs to be changed, else return the value
def nullify(value):
    x = value    
    if value is not None: #True null fields are read as None types
        if type(value) == str:
            if value.lstrip(' ') == '' or value.lower() == '<null>':
                x = None
        else: 
            if value == 0:
                x = None 

return x

if count > 0:
     #We're only interested in certain types of fields
     fieldList = [f.name for f in arcpy.ListFields(fc) if f.type
                  in ["String", "SmallInteger", "Integer", "Double"]]


     with arcpy.da.UpdateCursor(fc, fieldList) as rows:
          for row in rows:                                    
               rows.updateRow([nullify(val) for val in row])

Since I'm most familiar with 10.1+, and cursors in general are a lot better in the da module, here's a potential solution. Currently, you are creating a cursor each time you change fields, which means you are taking a hit there. Furthermore, you are checking the field type for each record instead of just using the field type once to filter initially.

I've changed how Null values are checked, but I haven't thoroughly tested it to check for all possible values. For the small sample dataset I had, it worked @ 10.2.2.

#Return None if the value needs to be changed, else return the value
def nullify(value):
    x = value    
    if value is not None: #True null fields are read as None types
        if type(value) == str:
            if value.lstrip(' ') == '' or value.lower() == '<null>':
                x = None
        else: 
            if value == 0:
                x = None 

return x

#We're only interested in some fields
ftypes = ("String", "SmallInteger", "Integer", "Double")
fieldList = [f.name for f in arcpy.ListFields(fc) if f.type in ftypes]

with arcpy.da.UpdateCursor(fc, fieldList) as rows:
    for row in rows:
        vals = [r for r in row]
        nulled = map(nullify, vals)
        if vals != nulled: #Only update if the row actually needs to be changed.
            rows.updateRow(nulled)