Only sometimes, actually. DDoS can be used for all sorts of annoying things. To saturate bandwidth, or to cause massive server load and essentially cause it to "loose" the internet. The high load is usually caused by mass open connection requests to a specific port, like a mass brute force on SSH, or FTP, or sending thousands of bots to query a MySQL-based webpage hundreds of times. Bandwidth saturation is simply sending so much "noise" to the server that its connection is maxed out. SYN, UDP, and ICMP are notorious for this, and it won't matter what port they target in this case as it's only meant to tie up the bandwidth.
A lot of kiddies won't even care if the server goes completely offline, as they know that most datacenters place a monthly limit on the ammount of traffic a website can receive, and will simply try to push the server over that limit... thereby causing a highly-overpriced penalty for overages. They will do this with single websites as well, using much the same tactic... find a large file or download, and simply have their bots query that same file over and over until, bwammo, suspended city.
The last example can be somewhat controlled through systems like mod_evasive and bandwidth throttling (some download modules offer this, otherwise you may have to look into third-party systems like Squid). Even then, it's only good for so long... 2000 bots will cripple your servers bandwidth whether you have mod_evasive and bandwidth throttling in place or not. The other examples, sadly, can only be blocked by the datacenter at their primary router. As I mentioned, the Fireslayer firewall that is used by Ev1 is a great example of this. It monitors packets at a higher level than your server, and will engage when it detects a flood coming in. And what's an added bonus is that most of these systems kick in before your server's switch, so any excess bandwidth from the attack doesn't get added to your total.
If your Datacenter is not willing to work with you to help prevent these occurances (the off-site ones, that is) and they themselves are not properly protected from DDoS, then you should probably start peeking at the competition and see what they have to offer. There are literally hundreds of Datacenters out there, and it's a heavily competing market... it shouldn't be hard to find the same, or even a better plan than the one you are on now, but also have the added bonus of DDoS filtering.
