Large tables without clustered indexes -- a bad idea, or ok?

Question

We have several large tables that don't have clustered indexes, but do have primary keys and assorted other indexes. We're seeing issues that look like they are related to statistics even though there is a nightly update statistics job.
So my question is, does the existence of a clustered index impact other indexes or the update statistics process? Are our tables ok the way they are?
Adding clustered indexes would be a big project for non-development-related reasons so I would need to have good reasons to advocate for this.

Answer 1

RSingh,
"By default" is a confusing word here. If you do it with WIZARD, I agree. But with T-SQL,there is no space for by default, it can be anything.
I agree that I assumed here as I wont do much things with wizard. :)
Try the below:
--Here by default, its non-clustered
create table Test_table(Col1 int , Col2 int not null )
Create clustered index IX__Test_Table on Test_Table (Col1)
Alter table test_Table
Add Constraint PK_testTable
Primary Key (Col2);
Drop table test_table
--Here by default, its clustered
create table Test_table(Col1 int , Col2 int not null Primary key)
Create index IX__Test_Table on Test_Table (Col1)
Drop table test_table
Neither the word "By Default" is a confusing word nor it happens only in WIZARD. Let me clarify below. I said "When a primary key constraint is created it creates a unique clustered index by default". Run the below DDL and check whether
a clustered index is created or not. i.e
CREATE TABLE Persons
P_Id int NOT NULL,
LastName varchar(255) NOT NULL,
FirstName varchar(255),
Address varchar(255),
City varchar(255),
CONSTRAINT pk_PersonID PRIMARY KEY (P_Id,LastName)
Regards, RSingh
That did not really make any sense to my context as I am NOT against that it will create Clustered index, In fact, my code says the same. My point is only "By default" is confusing. 
Let me explain, what I mean "By default"....
Create index IX_Indexname on Tablename(Colname)
The above will create "non clustered index" BY DEFAULT. Any situation, the above would create only non-clustered irrespective of other indexes present in the table.
Hope the above is clear. May be its my way looking at "BY DEFAULT".