I have my blog website with alot of do-follow links posted. If i remove all those links do my search engine ranking gets down or not?
This won't make any difference. Links with nofollow do not change the way PR s distributed in your website. PR is still "transferred" to nofollow links, the linked to sites just don't get it. So you won't be "sending" any more PR to your internal pages and thus not affecting your internal pages PR or rankings.
It depends on many factors. First of all, if you have any traded or paid-for links on your site (banners, affiliate links, etc.) you should definitely
nofollow them. The webmaster guidelines are very specific in this: http://www.google.com/support/webmasters/bin/answer.py?hl=en&answer=66736
Concerning other links, you should take a look what is being linked to.
Nofollow should ideally be used for links that you do not necessarily vouch for. Followed links to related content on normal/trusted websites can't hurt you, and in fact it is often said that Google promotes it, maybe even rewarding you for linking out to respected sites with related subjects.
There is no official source confirming this, but since Google is all about finding the most relevant results, a followed link to a relevant site would only benefit the search results. It wouldn't surprise me at all if websites indeed get (a small) pagerank reward when they have some followed links to related sites.
Then of course there's links you have less control over. Many sites automatically nofollow links posted by users (in comments, in user profiles/signatures, etc.) because they don't know if they can vouch for them. In their perspective, it's better to prevent damage by nofollowing all external links than risking spammers coming over and placing affiliate links on the website, which might do damage to the site.
In many other cases though, like a couple of blogs I run, a lot of the comments are moderated anyway. If someone posts a comment with a link in the text or in their user info, I check to see what it is. That way, I can remove bad links and know that the links that do get through are good enough for me to not nofollow it.
In fact, I personally think using too much of nofollow only hurts the web in it's entirety, but that's another story. (<-- this link is nofollowed by StackExchange because they can't tell if it's a good link or not. However, in my opinion if this post would get like 5 upvotes or something that might tell them the link can't be all that bad, and in my opinion it should be followed. Keep on dreaming...)
So in short: ruthlessly nofollowing all your links might get rid of some bad links on your site, but on a whole I don't think it's the best solution. Start with paid/traded links and unmoderated user-submitted links and I think you've got 99% of it covered.
There's no such thing as "do-follow." At best it's just any link that doesn't have nofollow applied to it.
So what exactly are you referring to? If you've got a bunch of links on your site that look like
<a href="http://example.com" rel="dofollow">text</a>
...I can't imagine they're making any difference at all, good or bad.