Denial of service is an attack during which normal communications with resources are interrupted by disabling resource itself or infrastructure on which resource functionality is based.

Service request floods
Service or web application is flooded with requests until all resources are used up. Carried out by setting up repeated TCP connection to a system. Consumes resources on victims system until they are exhausted.
SYN Attack/Flood
Uses tree way handshake concept to attack victims system. Forging SYN packets with fake source address. When victims system responds to SYN it goes to fake system and reply never received. Waiting period ties up the victim system.
ICMP Flood Attack
With ICMP victim is required to process and respond to ICMP request using its resources. ICMP attacks include smurf attacks, ICMP floods, ping floods. They all flood victim with ICMP requests without waiting for repose.

Ping of Death
Old stile attack utilizing packets larger then 64 K

Attacker sends custom-crafted fragmented packets with offset value that overlaps during attempted rebuild. This makes target machine unstable.

Spoofs the IP address of target machine and send ICMP echo requests to broadcast address of intermediary sites. Intermediary sites amplify ICMP traffic back to the source IP.
Variation of smurf attack which uses UDP rather then ICMP
Land attack sends traffic to the target machine with the source spoofed as the target system itself. The victim with try to acknowledge request in the loop with no end.

Example of smurf attack against target with spoofed IP

sudo hping3 -1 --flood -a

SYN flood attack on port 80

sudo hping3 --flood -p 80 -S

Here is one more example on how to perform SYN flood against web server with IP address

hping3 -i u1 -S -p 80

-i – number of seconds between packets
-S – SYN attack
-p – Port number