external database and mobile web

do you mean Mobile websites or  mobile Apps?
Mobile websites are the same as other websites except for layout of theirdisplay - they all live on a server and access databases the same way.
Mobile Apps - that's probably another matter depends on what mobile (iPhone,android,Windows)

There is no difference in connecting a mobile web site to a database or a "standard" web site to a database.  If the server connection scripts work, then they work.  Any trouble experienced is likely due to poor coding.

or do you mean websites living on a mobile device?
MySQL databases are connected to by thier IP address, database name and username and password, so it shouldn't be a problem except for maybe performance

website on a server mobile web not apps.

There is no difference for mobile web/ desktop web and database connection?

eg a mobile web and sql2010 db can work just as well as desktop db connection?
i thought there was a problem

I would be carful.... there is a difference in how you connect to your database with a web app vs mobile NATIVE app.   It was pointed out that in some cases an app can look like a native but it is not, this would be a web view.   For this purpose, let's call that a non native as it is still browser based and relying on the server.     When you are relying on the server, you will use server side code like php or asp with connection strings and coding that talk with the database and can never bee seen by the end  user unless the site is hacked into where the hacker can get  access to files on the server.

With a native app, while you could have a connection string in the same fashion, you would not want to do this as breaking into the app program is possible and the last thing you want is having 1 million devices with connection strings and passwords that would be difficult to change with out an update to the app.  Therefor, your calls to a database in a native app will be via a web service you create.  Typically you will send some data to your server that would include parameters and keys, maybe even base64 encrypted.  Then on the server, you decrypt the base64, apply the parameters and verify with another key such as sha/md5.  Then you process the data on the server as if it were a web form and lastly return a response as json or xml that is then read by the native app to display content.

To answer more directly, "Can mobile web sites connect easily to an external database now?" You shouldn't.  Use a post to your server, scrub input and return json/xml to be read by the app.

@padas - sorry ???   mobile websites CAN connect in the same way as PC based websites and do.
 they are NOT mobile Apps.
jagguy said he was intrested in mobile website not mobile native app
I agree with your explanation about native apps.
but not mobile displayed websites.

chilternPC, please read my first line, there is a difference in how you connect to your database with a web app vs mobile NATIVE app.   Otherwise, a website is a website.  I explained the difference.

Like most everything on the web, it's all smoke and mirrors and there are multiple ways to get to the same visual end and just as many opinions on which way to do it.  As @jason1178 pointed out if what @jagguy experienced may be a coding issue.

eg a mobile web and sql2010 db can work just as well as desktop db connection?
i thought there was a problem

What specific problems were you having or worried about?  Security and speed are the two major areas I can think of outside of not working at all.  

I'm sure you can search for a more formal list of best practices.  But this is what I use of the top of my head.
Speed
1) Open and close your database.  Get the data you need, throw it into a variable or array, close the db then use the array to extract data you need in your code instead of multiple calls to the db.

2) Pull out only the data you need.  Instead of, "select * from myTable..." use, "select name, email from myTable..."

3) Avoid over using wild card searches in large text fields.  

4) Avoid a query that will send too many results at once and only using some of them.  

5) Learn to add index's.  However, this can also slow things down

6) Normalize your data.  

Security
1) Scrub your data.  If you are expecting a date, use your server side code to make sure the incoming data is a date.  If you are expecting text, use the code of your choice to take out or convert any single quotes, html like characters.

2) Use parameter queries

3) Use sha or hash of your choice to create a key on your posting page and use the same formula on the receiving page.   var=sha1(field1&field2&field3&secretword1&secretword2) This helps insure you know where the data is from.

4) Don't post your password on your questions in EE

4) Don't post your password on your questions in EE

Spoilsport.

so to summerise..
Author>>>website on a server mobile web not apps.
me>>>ok lets not mention mobiles app and confuse the question and just answer about  websites on mobiles.

Author>>>There is no difference for mobile web/ desktop web and database connection?
me>>>that's correct.

Author>>>eg a mobile web and sql2010 db can work just as well as desktop db connection?
i thought there was a problem
Me>>>>mobiles supporting  web browsers will use wi-fi or 3G or better the same as a laptop away from home., the only problem as Padas says is would be the speed of connection causing possible timeouts, and security (but that's true of a PC/laptop)

...3g - can be very slow.  Especially during prime time.  If you have a small database w/few users, treat wifi and mobile the same.  If you are on a shared data server such as godaddy where you are paying $2 to $20 for hosting, or have a large query, bigger database, lots of users... account for 3g by presenting less data and html.  The responsive sites that simply present the same data in a different format for mobile vs not mobile (whatever "mobile" is depending on your detection script) can cause 3g phone experiences to be slow.  Have you tried using 3g phone on this site?  I have an android galaxy almost done with 2 yr contract and I find this site hard to use on it.

We have done a good job here addressing and defining mobile and speed and security... But I'm not sure we have addressed the exact problem @jagguy is having or experienced.  Has this info overload helped you?